Answer
f is one-to-one,
$f^{-1}(x)=\displaystyle \frac{x-b}{a} ,\quad(a\neq 0)$
Work Step by Step
f is a linear function.
Linear functions with slope$\neq$0 are strictly monotonic.
By Th.5.7, they are one-to-one and have inverses.
To find the inverse,
1. swap f(x)=y and x:
$y=ax+b $
$x=ay+b$
2. Solve for y:
$x=ay+b\qquad /-b$
$x-b=ay, \quad /\div a\quad(a\neq 0)$
$y=\displaystyle \frac{x-b}{a}$
3. Replace $y $ with $f^{-1}(x):$
$f^{-1}(x)=\displaystyle \frac{x-b}{a},\quad(a\neq 0)$
