#### Answer

The inverse of $f$ is $g(x)=\frac{x}{6}$.

#### Work Step by Step

$f(x)=6x$
Set $y=f(x)$. Then
$y=6x$
Switching $x$ and $y$ in the equation, we have
$x=6y$
Divide by $6$ on both sides to get
$\frac{x}{6}=y$
The inverse of $f$ is $g(x)=\frac{x}{6}$.
The graphs of the function and its inverse are shown in the attachment.