Single Variable Calculus, Chapter 7, 7.1, Section 7.1, Problem 2

a.) How is the inverse function $f^{-1}$ defined if $f$ is a one-to-one function with domain $A$ and range $B$? What is the domain of $f^{-1}$? What is the range of $f^{-1}$?
b.) If you are given a formula for $f$, how do you find a formula for $f^{-1}$?
c.) If you are given the graph of $f$, how do you find the graph of $f^{-1}$?

a.) If $f$ is a function with domain $A$ and range $B$, then $f^{-1}$ has domain $B$ and range $A$. Thus, $f^{-1}$ is defined as $f^{-1} (y) = x$ or $f(x) = y$
b.) If we have an equation $y = f(x)$, we solve the equation for $x$ in terms of $y$ first, then replace $x$ and $y$. Thus we get the inverse function $f^{-1}(x)$.
c.) Suppose that the graph of $f$ is given, the graph of $f^{-1}$ can be obtained by reflecting the graph of $f$ about the line $y = x$