0580/41 Oct/Nov 2023, Question 9: Composite Functions

Part (ai) · 1 mark

Evaluate the cubic function f at x = 0.

1. 1f(0) = (0 + 1)(0 + 5)(0 − 4) = −20

Answer−20

Part (aii) · 2 marks

Find the inverse of the linear function g.

1. 1Write y = 2x − 3, then swap x and y: x = 2y − 3
2. 2Add 3: x + 3 = 2y
3. 3Divide by 2: g⁻¹(x) = (x + 3)/2

Answer(x + 3)/2

Part (aiii) · 2 marks

Work out the composite value of g applied to h(2).

1. 1h(2) = 4^(2 × 2 − 1) = 4³ = 64
2. 2g(64) = 2 × 64 − 3 = 125

Answer125

Part (b) · 2 marks

Solve for x when g is applied to 2x and set equal to 7.

1. 1g(2x) = 2(2x) − 3 = 7
2. 24x = 10, x = 2.5

Answer2.5

Part (c) · 3 marks

Simplify the sum of g(x²), g(g(x)) and 1.

1. 1g(x²) = 2x² − 3, gg(x) = 2(2x − 3) − 3 = 4x − 9
2. 22x² − 3 + 4x − 9 + 1
3. 3= 2x² + 4x − 11

Answer2x² + 4x − 11

Part (d) · 2 marks

Find the inverse of h evaluated at 16.

1. 1h⁻¹(16) is the value of x that makes h(x) = 16
2. 24^(2x − 1) = 16 = 4²
3. 3So 2x − 1 = 2, giving x = 1.5

Answer1.5

Part (e) · 3 marks

Expand the cubic product to identify coefficients a, b, c and d.

1. 1(3x + 1)(x + 5) = 3x² + 16x + 5
2. 2(3x² + 16x + 5)(x − 4) = 3x³ − 12x² + 16x² − 64x + 5x − 20
3. 3= 3x³ + 4x² − 59x − 20
4. 4a = 3, b = 4, c = −59, d = −20

Answera = 3, b = 4, c = −59, d = −20

More past-paper questions on composite functions

• 0580/42 May/Jun 2026 Q17 · 7 marks
• 0580/43 May/Jun 2026 Q18 · 8 marks
• 0580/42 Feb/Mar 2025 Q14 · 5 marks
• 0580/21 May/Jun 2025 Q14 · 8 marks
• 0580/23 May/Jun 2025 Q22 · 8 marks
• 0580/21 Oct/Nov 2025 Q18 · 4 marks