# Problem 3

Find $g(x)$, if it is known that

$$
f(x+1)=3-2 x \text{ and } f(g(x))=6 x-3
$$
Answer: $g(x)=4-3 x$.

## Solution.

Transform the first function to the form $f(x+1)=5-2(x+1)$. This makes it clear how this linear function "works" on its argument. It will act in the same way on the function $g(x)$. That is, $f(g(x))=5-2 g(x)=6 x-3$. From which $g(x)=4-3 x$.