Composition of Functions & Binary Operations

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

1. If f(x) = 2x + 1 and g(x) = x², then (f∘g)(x) =
2. If f(x) = x + 1 and g(x) = 2x, then (g∘f)(3) =
3. Composition of functions is:
4. If f, g, h are functions, then (f∘g)∘h = f∘(g∘h) shows that composition is:
5. A binary operation * on a set S is associative if:
6. A binary operation * on a set S is commutative if:
7. The identity element for the operation * on ℝ defined by a*b = a + b - ab is:
8. For the binary operation a*b = a + b - 3 on ℤ, the set ℤ is:
9. If f(x) = 1/x and g(x) = √x, then the domain of (f∘g) is:
10. For the operation a*b = ab/(a+b), the associativity can be checked. Is it associative?
11. If f(x) = x - 2 and g(x) = 3x, then f⁻¹∘g⁻¹ =
12. A binary operation is said to have an identity element if:
13. For a set S with operation *, an element a is invertible if:
14. The composition of two bijective functions is:
15. If (f∘g)(x) = x and (g∘f)(x) = x, then g is:
16. For f(x) = 2x³, find g(x) such that (f∘g)(x) = x:
17. The number of binary operations on a set with 2 elements is:
18. If f(x) = ax + b and g(x) = cx + d, then (f∘g)(x) =
19. For the operation a*b = a + b + ab on ℚ, the identity element is:
20. If f and g have the same domain and codomain, (f∘g) has the same:
21. The operation * on ℝ defined by a*b = max(a,b) is:
22. For invertible element a⁻¹ with identity e, a⁻¹*a =
23. If f: A → B and g: B → C are one-one, then (g∘f): A → C is:
24. The closure property for a binary operation means:
25. Review question for Composition of Functions & Binary Operations