Chapter 1 - Functions - 1.3 Inverse, Exponential, and Logarithmic Functions - 1.3 Exercises - Page 35: 21

a. $f^{-1}(x) = x/2$ b. $f(f^{-1}(x)) = 2(x/2)$ $f(f^{-1}(x)) = x$ $f^{-1}(f(x)) = 2x/2$ $f^{-1}(f(x)) = x$

a. To find the inverse of a function switch $f(x)$ with $x$ and replace $f(x)$ with $f^{-1}(x)$. $f(x) = 2x$ $x = 2f(x)$ $x = 2f^{-1}(x)$ $x/2 = f^{-1}(x)$ $f^{-1}(x) = x/2$ b. $f(f^{-1}(x)) = 2(x/2)$ $f(f^{-1}(x)) = x$ $f^{-1}(f(x)) = 2x/2$ $f^{-1}(f(x)) = x$