Question

Дана функция f(x)=x+4. Найдите функцию g, такую, чтобы выполнялось равенство f(g(x))=x.

Answer 1

$f(x)=x+4\\\\x=g(x)+4\\\\\boxed{g(x)=x-4}$

Answer 2

Finding the Function g(x) Given f(x) = x + 4

To find the function g(x) such that f(g(x)) = x, we can use the given function f(x) = x + 4 and solve for g(x).

First, let's express f(g(x)) and set it equal to x:

Step 1: Express f(g(x)): f(g(x)) = g(x) + 4

Step 2: Set f(g(x)) equal to x: g(x) + 4 = x

Step 3: Solve for g(x): g(x) = x - 4

So, the function g(x) that satisfies the equation f(g(x)) = x is g(x) = x - 4.

This solution ensures that when g(x) is plugged into f(x), the result will be x.