ПРОСТЕЙШИЕ И УДОБНЫЕ СПОСОБЫ ОПРЕДЕЛЕНИЯ ФУНКЦИЙ В МАТЕМАТИКЕ И ПРИМЕРЫ ГП В ОБЛАСТИ ЗНАЧЕНИЙ

Аннотация

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. ПРОСТЕЙШИЕ И УДОБНЫЕ СПОСОБЫ ОПРЕДЕЛЕНИЯ ФУНКЦИЙ В МАТЕМАТИКЕ И ПРИМЕРЫ ГП В ОБЛАСТИ ЗНАЧЕНИЙ Аннотация. В этой статье представлен общий и подробный обзор области определения и значений, которые многим читателям кажутся трудными. Введена возможность находить ответы на простые и сложные функции удобными методами. Ключевые слова: область определения, область значений, квадратичная функция, тригонометрические функции, линейные функции. 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. 7 30 International scientific journal ISSN: 2181-3906 «MODERN SCIENCE АND RESEARCH» 2023 VOLUME 2 / ISSUE 5 / UIF:8.2 / MODERNSCIENCE.UZ 1 The domain of linear quadratic and cubic functions like 7 31 f  x   k x  b , f  x   a x ²  b x  c , f  x   a x ³  b x ²  c x  t .... is always    ;   . This is simply because there are no exceptions to the values x can accept. 2. f  x   1 x 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 x  0 . 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 f  x   x 1  2 function. In this case, we work as x  2  0 and get x  2 . That is, when the denominator takes the number 2, it remains 0, so the number 2 should be removed from the inequality. Answer: D     ; 2   2 ;   . 4. Find the domain of the function zzzz 1) we do not pay attention to x  3 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) x ²  3 x  2  0 ; x  2 , x  1 is formed 3) We remove the numbers 2 and 1 from the numbers (-∞; ∞). And the following inequality is formed. D ; 1 1;2 2; Answer: f x  x 5. Let's pay attention to the definition area of the function . For functions under even roots, the only condition x  0 is enough. And the following answer is formed. Answer: D   0 ;   6. Find the area where f  x   x  3 is defined x3 0. x 3 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 3 x  6  0 . 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. 3x 6; x 6 3) Answer: International scientific journal ISSN: 2181-3906 «MODERN SCIENCE АND RESEARCH» 2023 VOLUME 2 / ISSUE 5 / UIF:8.2 / MODERNSCIENCE.UZ 8. Find the domain of the 7 32 f  x   x 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: