Chapter 6 - Inverse Functions - 6.1 Inverse Functions - 6.1 Exercises - Page 407: 23

The inverse function is $$f^{-1}(x)=\frac{5-x}{4}.$$

Let $y=f(x)=5-4x$. To find the inverse function we have to express $x$ in terms of $y$ and then $x=f^{-1}(y).$ Now he have $$y=5-4x\Rightarrow 4x=5-y\Rightarrow x=\frac{5-y}{4},$$ so $$f^{-1}(y)=\frac{5-y}{4},$$ Renaming $y$ back to $x$ we get $$f^{-1}(x)=\frac{5-x}{4}.$$