Question

Для некоторой функции f:X⊂R→Y⊂R известно, что f(3x+8)=9x+6. Докажите, что функция f(x) может быть представлена в виде: f(x)=Ax+B. Большое спасибо

Answer 1

Ответ:

Фото

Пошаговое объяснение:

Answer 2

Proof that f(x) can be represented as f(x) = Ax + B

To prove that the function f(x) can be represented as f(x) = Ax + B, we will use the given information that f(3x + 8) = 9x + 6.

Let's start by substituting x = (3x + 8)/3 into the equation f(3x + 8) = 9x + 6:

f((3x + 8)/3) = 9((3x + 8)/3) + 6

Simplifying the equation:

f((3x + 8)/3) = 3(3x + 8)/3 + 6

f((3x + 8)/3) = 3x + 8 + 6

f((3x + 8)/3) = 3x + 14

Now, let's substitute u = (3x + 8)/3:

f(u) = 3u + 14

We have now expressed the function f(x) in terms of u. To represent it in terms of x, we need to substitute back x = (3u - 8)/3:

f(x) = 3((3x + 8)/3) + 14

Simplifying the equation:

f(x) = 3x + 8 + 14

f(x) = 3x + 22

Therefore, we have shown that the function f(x) can be represented as f(x) = 3x + 22, which is in the form f(x) = Ax + B.

In conclusion, the function f(x) can be represented as f(x) = 3x + 22.