Functions - One-one, Onto, Bijective, Inverse Functions

Grade 12 Maths Higher — Functions - One-one, Onto, Bijective, Inverse Functions: 25 practice questions with instant scoring and explanations.

1. A function f: A → B is one-one (injective) if:
2. A function f: A → B is onto (surjective) if:
3. A bijective function is one that is:
4. If f: ℝ → ℝ is defined by f(x) = 2x + 3, then f is:
5. The function f(x) = x² on ℝ → ℝ is:
6. If f: ℝ → [0, ∞) is defined by f(x) = x², then f is:
7. If f: [0, ∞) → [0, ∞) is defined by f(x) = x², then f is:
8. For a function f to have an inverse f⁻¹, f must be:
9. If f: A → B is bijective and f⁻¹: B → A is its inverse, then (f⁻¹)⁻¹ equals:
10. If f(x) = 3x - 7, then f⁻¹(x) =
11. For the function f: {1, 2, 3} → {a, b, c, d}, the function f can be:
12. The function f(x) = eˣ from ℝ → (0, ∞) is:
13. If f: ℝ → ℝ defined by f(x) = x³ - x, then f is:
14. Which of the following functions is one-one on its domain?
15. If f: A → B is one-one and onto, and g: B → C is one-one and onto, then g∘f: A → C is:
16. The function f(x) = |x| from ℝ → ℝ is:
17. If f(x) = (x - 1)/(x + 2), then the domain of f⁻¹ is:
18. How many one-one functions are there from a set with m elements to a set with n elements (m ≤ n)?
19. If f and g are inverse functions, then f(g(x)) =
20. The function f: ℕ → ℕ defined by f(n) = n + 1 is:
21. Which function from ℝ to ℝ is bijective?
22. For f(x) = √(x - 2), the inverse function is:
23. If f is a bijection and A ⊆ Domain(f), then f(A) has cardinality:
24. The inverse of f(x) = e^(2x) is:
25. Function f: R→R, f(x) = 3x is: