Composition of Functions

Grade 12 Maths — Composition of Functions: 25 practice questions with instant scoring and explanations.

1. If f(x) = 2x and g(x) = x + 1, then (f ∘ g)(x) equals:
2. The composition (f ∘ g)(x) means:
3. If f(x) = x² and g(x) = x + 2, then (g ∘ f)(x) equals:
4. Is function composition commutative? That is, is (f ∘ g) = (g ∘ f)?
5. If f(x) = 3x and g(x) = 1/x, then (f ∘ g)(2) equals:
6. Function composition is associative: (f ∘ g) ∘ h = f ∘ (g ∘ h). This statement is:
7. If f(x) = √x and g(x) = x - 1, then the domain of (f ∘ g) is:
8. If (f ∘ g)(x) = 4x² + 4x + 1 and g(x) = 2x + 1, then f(x) equals:
9. If f(x) = 1/(x - 1) and g(x) = 2x, then (f ∘ g)(3) equals:
10. The composition of two bijective functions is:
11. If f(x) = e^x and g(x) = ln(x), then (f ∘ g)(5) equals:
12. If h(x) = (f ∘ g)(x) and h is differentiable, then h'(x) by chain rule is:
13. If f(x) = |x| and g(x) = x - 2, then (f ∘ g)(1) equals:
14. If (f ∘ g)(x) = x for all x in the domain, then g is called:
15. The domain of (f ∘ g) is:
16. If f(x) = sin(x) and g(x) = π x, then (f ∘ g)(1/2) equals:
17. If (f ∘ g)(x) = 6x - 8 and f(x) = 3x - 2, then g(x) equals:
18. The range of (f ∘ g) is:
19. If f(x) = 2x + 1 and g(x) = 3x - 5, then (f ∘ g)⁻¹(x) equals:
20. If f and g are increasing functions, then (f ∘ g) is:
21. If f is increasing and g is decreasing, then (f ∘ g) is:
22. The composition (f ∘ g ∘ h)(x) means:
23. If f(x) = x/(x-1) and g(x) = 1/x, then (f ∘ g)(x) equals:
24. If f(x) = √(x + 2) and g(x) = x², then (f ∘ g)(2) equals:
25. If f⁻¹ and g⁻¹ exist, then (f ∘ g)⁻¹ equals: