Chapter 1 | Functions and Graphs
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1.24 Find the inverse of the function f ( x ) =3 x /( x −2). State the domain and range of the inverse function.
Graphing Inverse Functions Let’s consider the relationship between the graph of a function f and the graph of its inverse. Consider the graph of f shown in Figure 1.39 and a point ( a , b ) on the graph. Since b = f ( a ), then f −1 ( b ) = a . Therefore, when we graph f −1 , the point ( b , a ) is on the graph. As a result, the graph of f −1 is a reflection of the graph of f about the line y = x .
Figure 1.39 (a) The graph of this function f shows point ( a , b ) on the graph of f . (b) Since ( a , b ) is on the graph of f , the point ( b , a ) is on the graph of f −1 . The graph of f −1 is a reflection of the graph of f about the line y = x .
Example 1.30 Sketching Graphs of Inverse Functions
For the graph of f in the following image, sketch a graph of f −1 by sketching the line y = x and using symmetry. Identify the domain and range of f −1 .
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