Appendix A - Section A.2 - The Inverse of a Function - A.2 Problem Set - Page 497: 45

$f^{-1}(x) = \frac{x-5}{3}$

$f(x) = 3x+5$ Let $f(x) = y$ $y = 3x+5$ Switch $x$ and $y$ and solve for $y$ $x = 3y + 5$ $x - 5 = 3y$ $y = \frac{x-5}{3}$ $f^{-1}(x) = \frac{x-5}{3}$ $f[f^{-1}(x)] = $ $f(\frac{x-5}{3}) = $ $3(\frac{x-5}{3}) + 5 = $ $x - 5 + 5 = x$