Inverse Function and Domain–Range Analysis

00:00 6 marks

Consider the function \(f(x) = \frac{2x-1}{x+3}\), \(x
eq -3\).

(a) Find the inverse function \(f^{-1}(x)\). [3]
(b) State the domain and range of \(f^{-1}(x)\). [3]

Part a

5 minutes 3 marks

Question

Find the inverse function \(f^{-1}(x)\). [3]

Hint Hint

Hint

Begin by writing \(y = \frac{2x-1}{x+3}\), multiply both sides by \(x+3\) to eliminate the fraction, solve for x, and then swap x and y.

Answer Answer
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Explanation Explanation

Answer Answer

Complete Answer

\(f^{-1}(x) = \frac{3x+1}{2-x}\)

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Part b

5 minutes 3 marks

Question

State the domain and range of \(f^{-1}(x)\). [3]

Hint Hint

Hint

Remember that the domain of the inverse function is the range of \(f(x)\) and the range is the domain of \(f(x)\).

Answer Answer
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Explanation Explanation

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Complete Answer

Domain: \(\mathbb{R} \setminus \{2\}\); Range: \(\mathbb{R} \setminus \{-3\}\)

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