Question 3

00:00 4 marks

Let $f(x) = \sqrt{x-2}$ for $x \ge 2$.
(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

Set $y = \sqrt{x-2}$ then swap x and y and solve for y.

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Explanation Explanation

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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 that the domain of $f^{-1}$ is the range of $f$ and the range of $f^{-1}$ is the domain of $f$.

Answer Answer
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Explanation Explanation

Answer Answer

Complete Answer

Domain of $f^{-1}$: $x \ge 0$; Range of $f^{-1}$: $y \ge 2$

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