Question

What is the inverse of f(x)= 3x-9

Answer 1

If $f^{-1}(x)$ is the inverse of $f(x)$, then

$f\left(f^{-1}(x)\right) = x$

Given

$f(x) = 3x-9$

composing with the inverse function gives

$f\left(f^{-1}(x)\right) = 3f^{-1}(x) - 9 = x$

Solve for the inverse:

$3f^{-1}(x)-9 = x \\\\ 3f^{-1}(x) = x+9 \\\\ \boxed{f^{-1}(x) = \dfrac x3 + 3}$