Functions – Composition, Inverse Functions, Real-Valued Functions

Grade 11 Maths Higher — Functions – Composition, Inverse Functions, Real-Valued Functions: 25 practice questions with instant scoring and explanations.

1. If f(x) = 2x and g(x) = x + 3, then (f ∘ g)(x) =
2. The composition of functions is:
3. For (g ∘ f)(x), the function f is applied:
4. If f(x) = x + 5 and f⁻¹(x) is the inverse of f, then f⁻¹(x) =
5. For a function to have an inverse, it must be:
6. If f(x) = 3x - 2, then f⁻¹(7) =
7. The property (f ∘ f⁻¹)(x) = x is known as:
8. For f(x) = 2x + 1, the inverse function is:
9. If f(x) = √x and g(x) = x², then (f ∘ g)(4) =
10. A real-valued function is one where:
11. The graph of f⁻¹ is the reflection of the graph of f across:
12. If f(x) = x³ and g(x) = ∛x, then (f ∘ g)(8) =
13. For the inverse of f(x) = 1/x to exist (x ≠ 0), f must be defined on:
14. If (f ∘ g)(x) = 6x + 1 and g(x) = 2x, then f(x) =
15. The domain of (f ∘ g)(x) is:
16. If f: [0, ∞) → [0, ∞), f(x) = √x, then f⁻¹(x) =
17. For f(x) = e^x, the inverse function is:
18. If f and g are real-valued functions, then f + g is defined as:
19. For functions f(x) = x + 2 and g(x) = x², find (g ∘ f)(x):
20. If f: ℝ → ℝ, f(x) = 2^x, then f⁻¹(8) =
21. The product of functions (f·g)(x) is defined as:
22. If (f ∘ g)(x) = (g ∘ f)(x) for all x, then f and g are called:
23. For f(x) = sin(x) restricted to [-π/2, π/2], the inverse is:
24. The quotient function (f/g)(x) is defined as f(x)/g(x) where:
25. If f(x) = |x| and g(x) = x - 1, then (f ∘ g)(2) =