Graphing the Inverse Function from the Graph of a Function

The graph in Figure 55 is that of a one-to-one function \(y = f(x)\). Draw the graph of its inverse function.

Solution Since the points \((-2,-1)\), \((-1,0)\), and \(( 2,1)\) are on the graph of \(f\), the points \((-1,-2)\), \(( 0,-1)\), and \(( 1,2)\) are on the graph of \(f^{\,-1}\). Using the points and the fact that the graph of \(f^{-1}\) is the reflection about the line \(y = x\) of the graph of \(f\), draw the graph of \(f^{-1}\), as shown in Figure 56.