0580/42 May/Jun 2025, Question 19: Domain and Range

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 6 marks

The question, in short

Given f(x) = x + 1, g(x) = 5 − 2x and h(x) = 2ˣ, evaluate functions, find a range from a given domain, and solve equations involving h and its inverse.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Find the value of f(−3).

1f(−3) = −3 + 1 = −2

Answer−2

Part (b) · 2 marks

For domain {−3, 0, 2}, find the range of g(x).

1g(−3) = 5 − 2(−3) = 11
2g(0) = 5 − 0 = 5, g(2) = 5 − 4 = 1
3Range = {11, 5, 1}

Answer11, 5, 1

Part (c) · 1 mark

Find x such that h(x) = 1/32.

12ˣ = 1/32 = 1/2⁵ = 2⁻⁵
2x = −5

Answer−5

Part (d) · 2 marks

Find x such that h⁻¹(x) = 3.

1h⁻¹(x) = 3 means x = h(3)
2x = 2³ = 8

Answer8

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