Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 293: 83

$ f^{-1}(x)=\dfrac{x-b}{m}$ ($m\ne 0$)

In order to compute the inverse function, we must "interchange" $y$ and $x$ and then solve for the "new" $y$ (which is $f^{-1}(x)$). Here, we have: $y=mx+b, m \ne 0$ Switch $x$ to $f^{-1} (x)$ and $y$ to $x$ in the function to obtain the inverse. $x=mf^{-1}(x)+b\\ (x-b)=mf^{-1}(x) \\ f^{-1}(x)=\dfrac{x-b}{m}$