Inverse Function and Domain/Range

00:00 4 marks

Let \(f(x)=\sqrt{x-2}\) for \(x\ge2\).
(a) Find \(f^{-1}(x)\). [2]
(b) State the domain and range of \(f^{-1}\). [2]

Part a

3 minutes 2 marks

Question

Find \(f^{-1}(x)\). [2]

Hint Hint

Hint

Swap \(x\) and \(y\) in \(y=\sqrt{x-2}\) and square both sides to solve for \(y\).

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Explanation Explanation

Answer Answer

Complete Answer

\(f^{-1}(x)=x^2+2\)

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Part b

2 minutes 2 marks

Question

State the domain and range of \(f^{-1}\). [2]

Hint Hint

Hint

Remember: the domain of \(f^{-1}\) equals the range of \(f\), and the range of \(f^{-1}\) equals the domain of \(f\).

Answer Answer
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Explanation Explanation

Answer Answer

Complete Answer

Domain of \(f^{-1}\): \(x\ge0\); Range of \(f^{-1}\): \(y\ge2\)

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