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Nov 2021 p13 q6
763
The diagram shows the graph of \(y = f(x)\).
On this diagram sketch the graph of \(y = f^{-1}(x)\).
Solution
The graph of the inverse function \(y = f^{-1}(x)\) is obtained by reflecting the graph of \(y = f(x)\) across the line \(y = x\). This means that for every point \((a, b)\) on the graph of \(y = f(x)\), there is a corresponding point \((b, a)\) on the graph of \(y = f^{-1}(x)\).
In the diagram, the curve \(y = f(x)\) is reflected over the line \(y = x\) to produce the curve \(y = f^{-1}(x)\).