Question

Use the given graph of\(f\)to sketch the graph\({f^{ - 1}}\).

Short answer

The graph of \({f^{ - 1}}\) is shown below:

Step-by-step solution

Condition for the graph of \({f^{ - 1}}\) 

The graph of \({f^{ - 1}}\) is determined byreflectingthe graph of \(f\) about theline \(y = x\).

Sketch the graph of \({f^{ - 1}}\)

Reflect the graph of \(f\) about the line \(y = x\) to get the graph of \({f^{ - 1}}\).

Use the graph of \(f\) to sketch the graph of \({f^{ - 1}}\) as shown below:

The points \(\left( {0,1} \right),\left( {2,0} \right)\) on the graph of \(f\) are reflected to the points \(\left( {1,0} \right)\left( {0,2} \right)\) on the graph of \({f^{ - 1}}\).

Thus, the graph of \({f^{ - 1}}\) is obtained.