Question

If f(x) = 2x + 10, then f^-1(x) =

Answer 1

If
`f^(-1)(x)` is the inverse of
`f(x)`, then

`f\left(f^(-1)(x)\right) = x`

by definition of inverse function. We have

`f\left(f^(-1)(x)\right) = 2f^(-1)(x) + 10 = x`

Solve for the inverse :

`2f^(-1)(x) + 10 = x \\\\ 2f^(-1)(x) = x-10 \\\\ \boxed{f^(-1)(x) = \frac{x-10}2}`