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 :

$2f^{-1}(x) + 10 = x \\\\ 2f^{-1}(x) = x-10 \\\\ \boxed{f^{-1}(x) = \dfrac{x-10}2}$