Abstract: This article provides a general and detailed overview of the area of definition and values that many readers find difficult. The ability to find answers to simple and complex functions using convenient methods is introduced.

Key words: Domain of definition, domain of values, quadratic function, trigonometric functions, linear functions

Another important issue that always comes to our mind is related to the manners, behavior and, in a word, worldview of our youth. Today, times are changing rapidly. Those who feel these changes the most are young people. Let the youth be in harmony with the demands of their time. But at the same time, he should not forget his identity. Let the call of who we are, the descendants of great people always echo in the heart of the file and encourage us to stay true to ourselves. What can we achieve? Education, education and only education. (I.A. Karimov.)

Every person wants the science he studies to be more perfect and looks for its favorable aspects, works tirelessly on himself, as it can be seen that every science and field has its own difficulties and aspects to consider. For example, let’s look at mathematics, from afar it seems difficult and sometimes impossible, but if we look closely at mathematics, it becomes much easier to understand its beauty and meaning. As a proof of this, we will provide information about the simplest and most convenient methods of defining functions and examples in the field of values in mathematics. First, “What is a domain of definition and a domain of values?” Let’s form general ideas about this concept. That is, we do not abstract certain concepts in our brain with the rule. Actually the rule confuses the point, this is my personal opinion. 

The field of definition is the values that the function can accept, and the expression formed by these values is called the field of values of the function. As a clear example of this, we will get acquainted with the following functions. First, let’s get acquainted with examples related to the field of detection.

1 The domain of linear quadratic and cubic functions like …. is always . This is simply because there are no exceptions to the values can accept.

2. What is the domain of the function? We find a solution to this as follows. It cannot accept only the number 0 in the denominator. That is, it satisfies all values other than 0. We set the condition . This results in the following inequality. We remove the number 0 from the numbers up to and get the following inequality.

Answer: D=(-∞; 0) (0; ∞)

3. Let’s find the field of definition for the function. In this case, we work as and get . That is, when the denominator takes the number 2, it remains 0, so the number 2 should be removed from the inequality.  

Answer: .

4. Find the domain of the function zzzz

1) we do not pay attention to in the picture. We only find the definition area for the denominator. The domain of definition in the denominator is valid for an entire function.

2) is formed

3) We remove the numbers 2 and 1 from the numbers (-∞; ∞). And the following inequality is formed.

Answer: 

5. Let’s pay attention to the definition area of the function . For functions under even roots, the only condition is enough. And the following answer is formed.

Answer: 

6. Find the area where is defined

1) is formed

Answer: 

7. Find the domain of the function f(x).

1) we apply the expression under the root according to the above rule.

2) We give the condition . Why is the inequality sign > instead of The reason is very simple, if the sign is non-deterministic, a value will be generated that will make the denominator 0, so we specify a non-deterministic sign.

3) 

Answer: 

8. Find the domain of the function

1) An even number always appears under the module. We can say that this is an invariant axiom. That is, it is an opinion that does not require any proof.

2) So the expression under the module can accept any number.

Answer: (-∞; ∞)

9. Etc., the field of definition of functions of the form takes values (-∞;0) (0; ∞).

Answer: 

10. The definition area of . functions is accepts numbers up to That is, is always valid in all values.

Answer: 

But there are some exceptional cases. Let’s take a look at them. For example, given a function , a very simple solution is the same as the function with domain of definition. That is, is formed. Don’t get distracted by one thing, it’s not good to rush to assume that the function is always . Regardless of what function is given, we should always pay attention to the values that can take.

Or consider the function .

1) It is enough to find the domain of the function

2) is formed.

  The domain of the function is (-∞; ∞), the numbers 3 and 1 are removed and the following answer is obtained.

Answer  

Let’s look at examples from the field of values.

1. Find the domain of the function . 

1) The example is solved by replacing the expressions and with numbers.

2) this expression has a solution for all real values of It can go on like this.

Answer: 

2. Find the domain of the function .

1) A, b, c expression is replaced by a numerical value

2) 

3) is derived from the expression. 

4) The expression is equal to 0. 

5) The expression is substituted for the expression 

6) 

7) means, after satisfying the condition , the answer is . If , it would be the opposite, i.e. 

Answer: 

3. Find the domain of the function  

1) Let’s think a little through this example condition. When the denominator is 0, the expression has an unacceptable range of values.

2) This expression produces . And this number 0 is removed from the number line. And the following response is generated.

Answer: 

4. We try to find the range of values of the expression . Based on the reasoning above, the denominator should not be 0, and we should exclude that number from the answer.

1) is formed

Answer: 

5. Find the domain of the function  

1) Such examples are actually very simple. It is necessary to understand the way of work, not to memorize it. These simple examples are the basis for working on difficult examples.

 Let’s look at the range of values of functions .

1) in these functions, which we have seen above, is an unknown number of arbitrary infinite values.

2) but always has values even when it is any infinite number

Answer: 

7. Find the domain of the functions. Among the functions, the most simple way to find the values and the field of determination is precisely these functions.

Answer: 

Conclusion: The methods and recommendations given in this article about the examples and problems given in the field of values and the field of definition are very useful. In the society we live in, many things seem complicated, but everything is very easy. It is only necessary to know how to place these complexities in the child’s mind and to have the right psychological approach. Taking into account his nature and thinking, a certain topic should be explained in a childish way in the language he is interested in.

References:

1. Karimov I.A. “A perfect generation is the foundation of the development of Uzbekistan” Tashkent: Spirituality 1997.

2. Jumayev M.E., Tajiyeva Z.G. “Methodology of teaching mathematics in primary grades” Tashkent: science and technology, 2005.

3. Toshboyeva, S. R., & Turg’unova, N. M. (2021). THE ROLE OF MATHEMATICAL OLYMPIADS IN THE DEVELOPMENT OF INDIVIDUAL CONSCIOUSNESS. Theoretical & Applied Science, (4), 247-251.

4. Toshboyeva, S. R., & Shavkatjonqizi, S. M. (2021). Specific ways to improve mathematical literacy in the process of sending students to hinger education. Academicia: An international multidisciplinary research journal, 11(10), 234-240.

5. Toshboyeva, S. R. (2020). Competent approach in teaching probability theory and mathematical statistics. EPRA International Journal of Research and Development (IJRD).

6. Rahmonberdiyevna, T. S., & Soxibovna, A. M. (2021). Techniques for Teaching Elementary Students Rational Numbers and Convenient ways to Perform Operations on Them. International journal of culture and modernity, 11, 283-287.

7. Raxmonberdiyevna, T. S., & Shavkatjonqizi, S. M. (2021). Methods for the development of stochastic competence in mathematics lessons at school. ACADEMICIA: An International Multidisciplinary Research Journal, 11(5), 863-866.

8. Rakhmonberdiyevna, T. S. (2022). CREATIVITY AS A PEDAGOGICAL PROBLEM. Conferencea, 138-141.

9. Rakhmonberdiyevna, T. S. (2022). RESEARCH OF CREATIVE ACTIVITY OF THE FUTURE PRIMARY CLASS TEACHER. Conferencea, 155-157.

10. Rahmonberdiyevna, T. S. (2022). MULOHAZALAR VA PREDIKATLAR USTIDA AMALLAR MAVZUSI BO ‘YICHA BA’ZI MASALALARNI YECHISHNING SODDA YO ‘LLARI. RESEARCH AND EDUCATION, 1(2), 234-237.

11. Тошбоева, С. Р. (2022). БЎЛАЖАК БОШЛАНҒИЧ СИНФ ЎҚИТУВЧИЛАРИНИНГ ИЖОДИЙ ҚОБИЛИЯТЛАРИНИ РИВОЖЛАНТИРИШНИНГ НАЗАРИЙ АСОСЛАРИ. Journal of new century innovations, 4(1), 294-297.

12. Тошбоева, С. Р. (2022). БЎЛАЖАК БОШЛАНҒИЧ СИНФ ЎҚИТУВЧИЛАРНИНГ ИЖОДИЙ ҚОБИЛИЯТЛАРИНИ МАЛАКАВИЙ АМАЛИЁТ ЖАРАЁНИДА РИВОЖЛАНТИРИШНИНГ ПЕДАГОГИК ХУСУСИЯТЛАРИ. Journal of new century innovations, 4(1), 289-293.

13. Toshboeva, S. R., Mallaboeva, B. M., & Yusupova, L. A. K. (2022). LAWS AND THEIR APPLICATION BASED ON SOME INTERESTING COMBINATORIAL PROBLEMS. Oriental renaissance: Innovative, educational, natural and social sciences, 2(10), 1341-1349.

14. Rahmonberdievna, T. S., & Mukhtorovna, M. B. (2022). LAWS AND THEIR APPLICATION BASED ON SOME INTERESTING COMBINATORIAL PROBLEMS.

15. www.pdffactory.com.

Spring

You are the season of youth, this world will bright,
Fields live in a green world,
I sing for you, pen in hand,
Bring joy to hearts, spring!

Bring confidence to hearts, spring,
Bring peace and harmony, spring,
Come and pick the flowers of goodness, spring,
Bring happiness and joy, spring!

When the apricot blossoms, these gardens are white,
The mountains are full of crimson tulips,
This spring leads to sweet dreams,
Spring is the bride of the seasons.

Aminova Ogiloy was born on October 15, 2008 in the Yoshlik neighborhood of the Tortkol district of the Republic of Karakalpakstan. Young poet and reader. Her creative works have been published in countries such as Turkey, Great Britain, USA, Canada, Australia, Thailand, and India.

I AM FROM UZBEKISTAN

I am your poet child
If you give me wings, I will fly to the sky
Mother says I love my country
My voice is ringing today.
Make a pen and paper an excuse
Expressing my love from the bottom of my heart
My blood flows in my veins
My homeland is connected to your veins.
You are burning in my heart
I will not write you poems
That's when my pen broke
I'd rather go beyond Sharia.
How would my Uzbeg describe you?
The pen is incapable of writing your tariff
Only one pain remained in my heart
My name as a poet is painful.

One day in class…

As Allah bestows great miracles on our hearts, we need to live with a sense of gratitude for this blessing. gives…

I still remember the first day I came to work at the great dargah called the school… As I entered the door of this dargah, whose threshold is the paths of the paradise of knowledge, I was very proud to be a student of my grandmother, whose places are from heaven in my heart, and my kind teacher mother.

From the door of the classroom, I heard the excited shouts of the students: “Here, a new teacher has arrived.” I was happy with this call… We started the lesson with the young generation who always honors their homeland and discovers new aspects of creativity in themselves. First of all, I got to know the students.

During the lesson, only one student caught my attention. Congratulations, as you can see, there are always students who are not interested in class and do not complete their homework on time. And, I have come to a decision. As I got to know him better, I made sure that he also has interests and dreams. My student is interested in mother tongue, science, English. In his free time, he likes to draw and read art books. While he was talking to me, sweat covered his forehead, I felt that he was thinking about his words and talking shyly.

So, I found out that my student is shy and shy, he doesn’t even have a close friend. My classmates also confirmed my opinion. From that day on, I started helping my student with his homework, under the pretext of trying to get to know him better. And I always told him that he is not inferior to his friends, that he should always strive forward, believe in his own strength and knowledge. I dealt with the student. If you believe now, this student has become the most active student of the school. In particular, I was able to awaken in his heart a feeling of interest in special creativity. Nowadays, this student does not like to write wonderful poems and stories from each other. These are the words…

Mamatgosimova Sitora Bakhtiyor is a promoter of creative and cultural issues of the 34th general education school of Boyovut district, Sirdarya region.

What is happiness for you?

Everyone imagines happiness differently, but the scope of this concept is much wider than our scope of thinking and it cannot be expressed in a single case. Let's say that the birth of a person
is happiness, marrying someone you love is happiness, and having children is happiness. Also, receiving parental blessings is happiness for a child, to have a car, to build a house, to achieve some other dreams... They are, all of them can be happiness for some people. 

These states, which people know as happiness, can be continued as long as they want. But there is such happiness among them that to be a guest of it is a great example of perfection. This is to be loyal to the Motherland, to show self-sacrifice for the development of society, peace, and tranquility of compatriots. Also, happiness can be, to love people, to look at them impartially, with the eyes of love, to recognize that everyone is a person like himself and that they are equal
before the Creator. Even greater happiness for me is that I am a young generation of a peaceful country called Uzbekistan.

The word "Motherland" itself has a broad meaning. Our world is one of the meadows, where nature is our land, and faith in God is a blessing. Unfortunately, many estimate happiness to be wealth in this life. Wealth is not an indicator of happiness. For example, a great Russian scientist saw his happiness in creating rockets. He lived by eating leftovers from kitchens. But even in such conditions, he considered himself happy. Being full can be a small factor in feeling happy.

Satisfying human needs at least to a moderate level also creates the basis for happiness. Sometimes even people who have enough of everything feel unhappy. What should people do to feel happy?

Coming into this world as a human is happiness, and leaving it as a human is even more happiness. Nonetheless, we are not always able to appreciate the value of happiness. Getting up early to see the sunlight and breathing every moment of our life is unlimited happiness. It's about being able to feel it and enjoy the blessings of the world.

"Happiness cannot be traveled to, owned, earned, worn, or consumed. Happiness is the spiritual
experience of living every minute with love, grace, and gratitude." 
-- Denis Waitley

Nobody is perfect

Everyone think I'm perfect, that I have a perfect family, that I have good friends, but one thing is for sure! That's fk bullshit! My life is far from perfect! Everyone keeps asking "how can you not have a boyfriend? You are perfect! You are beautiful, all the boys want you! You have a good body, you are so sweet and you only want the best for others" and yes, ofc I do! Bc I know what it's like to treated like shit! NO, I'm NOT perfect!

Nothing about me is perfect! NO all the boys don't want me! I am broken! Everything I have been through has destroyed me inside! I'm not the same as I was yesterday, I'm not the same as I was a week ago, a month ago or a year ago! I do not know who I am, I do not know what I want, I do not know who my friends are, I can't live with my family! Nothing in my life is perfect! My whole world is laughing! The only thing I want for others is the best, be I don't want them to end up like me! I put on a face, so people don't see any other thing that a happy me! No one should see the truth. People won't understand! It anyway! All I do is wait! Wait for something good to happen, wait for me to find myself! But now it doesn't seem to happen! That's just how people are born!

Someone is happy, someone is unhappy and some people are just waiting!

One day..

One day, he'll know. He'll know your birthday, your middle name, your parents' names and where you were born. He'll know your zodiac sign, your eye color, how many scars you have and how you got them. He'll know how many cousins you have and how old you were when you first learned how to ride a bike and exactly how many freckles you have. He's going to know your favorite book, movie, song, food, pair of shoes and color. He'll know your dreams and why you can't sleep at night. He'll understand why you worry about irrelevant things. He'll know that when that one song comes on, he'd better turn it up. He's going to memorize your facial expressions, your laugh when you really think something is funny and the bad habits you wish you could break. He'll know how you don't want to get any older, how much you love golden hour and when the sun sets or rises. He's going to know how many kids you want and what colors you want in your wedding and how you wish you could tell all the people that you hurt how sorry you are. He'll know that you like your coffee with cream and sugar and lots of it. He'll know that it takes you forever and a day to decide where you want to eat and exactly what ice cream you like to order because you never change it. He's going to know how you dance, kiss, smile, walk and sing. He'll figure out what to do when you can't stop crying and he'll know exactly what's wrong before you tell him. One of these days he's going to know everything there is to know about you and he's going to love all of it.

So, be patient and wait for the right person.

THE ACTIVITIES OF INTERNATIONAL EMBASSIES IN UZBEKISTAN

Abstract: The Republic of Uzbekistan conducts an open, mutually beneficial and constructive foreign policy based on its national interests. The modern transport political course of the republic is formed based on the rapidly changing situation in the world and
in the region, as well as large-scale changes within the country. In this article, we will talk about International Embassies in Uzbekistan We will cover the topic of embassies in detail.

Key words: Embassies, international relations, diplomatic cooperation, states, documents, historical works, international meetings.

There are about 39 Foreign Embassies and 6 Consulates placed in the territory of Uzbekistan. At present, the capital of Tashkent hosts 44 embassies. Embassies, trade missions with diplomatic status, President Ilhom Aliyev laid a wreath at the statue of the great leader Heydar Aliyev in front of the center. During the acquaintance with the
building, it is located on Haydar Aliev street in the center of Mirabad district of Tashkent, where Azerbaijanis live compactly. It was informed that there are museums of Heydar Aliyev, the history of Azerbaijan statehood, mutual friendship of Azerbaijan and
Uzbekistan in the center. 

President Ilhom Aliyev was the first to get acquainted with the Heydar Aliyev Museum. In it materials reflecting different periods of the national leader's life and activities, photo documents immortalizing his meetings with state leaders, opinions of famous people about Heydar Aliyev have been collected. During his visit to the Museum of the History of Azerbaijan Statehood, President Ilhom Aliyev was given detailed information about the maps, historical documents, and famous people of our republic, which once occupied an area of 400,000 square kilometers.

The exhibits collected in the Museum of Friendship of Azerbaijan and Uzbekistan speak about the ancient historical and cultural relations between our countries, as well as the current developing relations. President Ilhom Aliev inspected the conference hall of
the Center. It was announced that Azerbaijani music, dance and folklore ensembles will also perform in the cultural center in the future. In addition, an Azerbaijani school and a library were established here. After getting acquainted with the center, President Ilhom Alive met with members of the Azerbaijani diaspora. 

Congratulating our compatriots on the occasion of the opening of the center, our President said: - I congratulate you from the bottom of my heart. I congratulate the opening of this wonderful cultural center after a major renovation. Six years ago, we celebrated the opening of the Azerbaijan Cultural Center here together with the honorable teacher Shavkat. If the building of that time was probably acceptable for that time, it is certainly more suitable for today.

Therefore, it was decided to completely renovate this cultural center, and with the direct participation of the embassy, with the great support of the Uzbek government, a very beautiful, magnificent, magnificent center was created. I mean, this cultural center
has more than six years of history, but today its new era is beginning.

Because major renovation works were carried out with very high quality and taste. This center is, in fact, a symbol of Uzbekistan-Azerbaijan friendship. The Uzbekistan-Azerbaijan Friendship
Museum also operates in this center. This center is named after the great leader Heydar Aliyev. And this is very meaningful. Because the head of the great state Heydar Aliyev has always made great efforts to develop relations between Azerbaijan and Uzbekistan.

During the Soviet period, the relations between our peoples were very close, built on the basis of brotherhood, especially during the period of independence, the leaders of the two countries played a very important role in reaching the current level of mutual relations. In
other words, our friendship has a long history and historical roots. As independent countries, Uzbekistan and Azerbaijan have raised this cooperation to a higher level in recent years. 

The participants of the event once again expressed their gratitude to the President of Azerbaijan for his contribution to the development of friendly and brotherly relations between our nations. Then a souvenir photo was taken. After that, President Ilhom Aliyev visited the exhibition of the works of the late Azerbaijani sculptor Eynulla
Aliyev who lived in Samarkand, organized in the exhibition hall of the Cultural Center.

Strategic cooperation between Uzbekistan and Russia signed on June 16, 2004, agreements on alliance relations of November 14, 2005 and deepening of strategic cooperation between the Republic of Uzbekistan and the Russian Federation signed on
June 4, 2012 comprehensive strengthening and gradual development of friendly relations on the basis of the declaration is fully in line with the interests of the two countries and serves to strengthen peace and security in the region.

The most important tasks of bilateral relations are to complete the agreements reached during the state visit of the President of the Republic of Uzbekistan Sh.M. Mirziyoyev to Russia on April 4-5, 2017 and the state visit of the President of the Russian Federation V.V. Putin to Uzbekistan on October 18-19, 2018. is to ensure its
implementation. Particularly Germany, France, Great Britain, Belgium, Italy, Spain, Latvia and other countries to a higher level. 

Our republic consistently pursues a policy aimed at strengthening friendship and cooperation with the state of Turkey, which has a
centuries-old common history, common language and religion, common values and similar traditions. Our country will develop mutually beneficial cooperation with Turkey, including trade, investment and tourism.

References:
1. https://advice.uz/oz/document/1621
2. http://azculture.uz/uz/bizim-markaz.php?link=markazin-ochilishi
3. https://www.amerikaovozi.com/a/a-36-2006-02-24-voa3-
93345049/795730.html
4. http://www.uzbekistan.org.ua/uz/o-zbekiston-respublikasi-tashqisiyosati.html 
5. https://en.m.wikipedia.org/wiki/List_of_diplomatic_missions_in_Uzbekist
an#:~:text=At%20present%2C%20the%20capital%20of%20Tashkent%
20hosts%2044%20embassies.
6. A new embassies along An Ancient Route in Uzbekistan written by
HENRY L CLARKE (Author)

1. Ahmedov Azimjon-The teacher of
Andijan State Institute of Foreign
Languages
2. Honazarova Odina Dostonbek's
daughter - The student of Andijan State
Institute of Foreign Languages 301-Guide
followship and interpreting activities