#### Answer

$f(x)=4x-12$
$f^{-1}(x)=\dfrac{x+12}{4}$

#### Work Step by Step

$f(x)=4x-12$
Substitute $f(x)$ by $y$:
$y=4x-12$
Solve the equation for $x$. Do so by taking $12$ to the left side and rearranging the equation:
$y+12=4x$
$4x=y+12$
Take $4$ to divide the right side:
$x=\dfrac{y+12}{4}$
Interchange $x$ and $y$:
$y=\dfrac{x+12}{4}$
Substitute $y$ by $f^{-1}(x)$:
$f^{-1}(x)=\dfrac{x+12}{4}$
The graph of both the original function and its inverse is shown in the answer section.