#### Answer

$f(x)=8-4x$
$f^{-1}(x)=\dfrac{8-x}{4}$

#### Work Step by Step

$f(x)=8-4x$
Substitute $f(x)$ by $y$:
$y=8-4x$
Solve the equation for $x$. Start by taking $4x$ to the left side and $y
$ to the right side:
$4x=8-y$
Take $4$ to divide the right side:
$x=\dfrac{8-y}{4}$
Interchange $x$ and $y$:
$y=\dfrac{8-x}{4}$
Substitute $y$ by $f^{-1}(x)$:
$f^{-1}(x)=\dfrac{8-x}{4}$
The graph of both the function and its inverse is shown in the answer section.