Question

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

Short answer

The points \(\left( { - 1, - 2} \right),\left( {1, - 1} \right),\left( {2,2} \right)\), and \(\left( {3,3} \right)\) on the graph of \(f\) are reflected to the points \(\left( { - 2, - 1} \right),\left( { - 1,1} \right),\left( {2,2} \right),\) and \(\left( {3,3} \right)\) on the graph of \({f^{ - 1}}\).

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 \(\left( { - 1, - 2} \right),\left( {1, - 1} \right),\left( {2,2} \right)\), and \(\left( {3,3} \right)\) on the graph of \(f\) are reflected to the points \(\left( { - 2, - 1} \right),\left( { - 1,1} \right),\left( {2,2} \right),\) and \(\left( {3,3} \right)\) on the graph of \({f^{ - 1}}\).