0580/21 Oct/Nov 2024, Question 18: Inverse Functions
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 3 marks
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The question, in short
For g(x) = 4^(x + 3), find the x giving g(x) = 1, and evaluate the inverse function g⁻¹(1/16).
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Part (a) · 1 mark
Solve 4^(x + 3) = 1 for x.
- 14^(x + 3) = 1 = 4⁰
- 2x + 3 = 0 → x = −3
Answer−3
Part (b) · 2 marks
Find the value of g⁻¹(1/16) for g(x) = 4^(x + 3).
- 1g⁻¹(1/16) is the value of x that makes g(x) = 1/16
- 21/16 = 1/4² = 4⁻², so 4^(x + 3) = 4⁻²
- 3x + 3 = −2, giving x = −5
Answer−5
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Also searched as: 0580/21/O/N/24 · 0580_w24_qp_21 · 0580 w24 21 · question 18.
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