Answer
$f^{-1}(x)=\frac{x}{m}-\frac{b}{m}$
Work Step by Step
If I want to find the inverse of a function, then I first must express $x$ from the function. Then, switching $x$ to $f^{-1}(x)$ and $y$ to $x$ in the function basically gives the inverse.
$y=mx+b$, $m\ne0$. Thus: $y=mx+b\\y-b=mx\\\frac{y}{m}-\frac{b}{m}=x$.
Hence $f^{-1}(x)=\frac{x}{m}-\frac{b}{m}$
