JEE Main - Composition of functions Online Test (MCQ Quiz)

1. If f(x) = 2x + 3 and g(x) = x^2, find the composition (f o g)(x).

A) 2x^2 + 3 B) 4x^2 + 9 C) (2x + 3)^2 D) 2(x^2 + 3)

2. Given f(x) = x - 1 and g(x) = 3x, find the composition (g o f)(x).

A) 3x - 1 B) 3(x - 1) C) x - 4 D) 3x - 3

3. Let f(x) = x^2 and g(x) = x + 1. Which of the following is equal to (f o g)(x)?

A) x^2 + 1 B) (x + 1)^2 C) x^2 + x + 1 D) x^2(x + 1)

4. If f(x) = 1/x and g(x) = x - 2, find (f o g)(x).

A) 1/(x - 2) B) (1/x) - 2 C) 1/x - 1/2 D) x - 1/2

5. What is the domain of the composite function (f o g)(x) if f(x) = sqrt(x) and g(x) = x - 3?

A) x >= 0 B) x >= 3 C) x >= -3 D) x >= -infinity

6. Let f(x) = sin(x) and g(x) = x^2. Find (f o g)(pi/2).

A) sin(pi^2/4) B) 1 C) 0 D) sin(pi/4)

7. If f(x) = 2x and g(x) = x/2, what is (f o g)(x)?

A) x B) 2x C) x/2 D) 4x

8. Given f(x) = e^x and g(x) = ln(x). What is (f o g)(x)?

A) x B) e^x ln(x) C) ln(e^x) D) e^(ln(x))

9. If f(x) = x^2 + 1 and g(x) = sqrt(x - 1), find the domain of (f o g)(x).

A) x >= 1 B) x >= 0 C) All real numbers D) x <= 1

10. Let f(x) = x - 5 and g(x) = x + 5. What is (f o g)(x) - (g o f)(x)?

A) 0 B) 10 C) -10 D) 2x

11. If f(x) = 3x - 2 and g(x) = (x+2)/3, find (f o g)(x).

A) x B) 3x C) (x+2)/3 D) x - 2

12. Consider f(x) = |x| and g(x) = x^2. What is (g o f)(x)?

A) |x^2| B) |x|^2 C) x^2 D) |x|

13. If f(x) = x^3 and g(x) = x^(1/3), what is (f o g)(x)?

A) x B) x^(3/2) C) x^(1/9) D) x^3

14. Let f(x) = 2x + 1 and g(x) = x^2 - 1. Find (g o f)(2).

A) 15 B) 24 C) 48 D) 16

15. If f(x) = ax + b and g(x) = cx + d, find (f o g)(x).

A) acx + ad + b B) acx + bc + d C) acx + bd D) acx + ad + cd + b

16. What is the range of the composite function (f o g)(x) if f(x) = x^2 and g(x) = x - 1?

A) y >= 0 B) y >= -1 C) All real numbers D) y >= 1

17. Let f(x) = 1/(x-1) and g(x) = x+1. Find the domain of (f o g)(x).

A) x != 0 B) x != 1 C) x != -1 D) All real numbers

18. If f(x) = 3 and g(x) = x^2 + 1, what is (f o g)(x)?

A) 3x^2 + 1 B) 3(x^2 + 1) C) 3 D) x^2 + 4

19. Given f(x) = x^2 - 4 and g(x) = sqrt(x). Find (g o f)(3).

A) sqrt(5) B) 5 C) 3 D) sqrt(3)

20. If f(x) = 2x and g(x) = 3x, what is (f o g)(x)?

A) 5x B) 6x C) 2x + 3x D) x

21. Let f(x) = x + 7 and g(x) = x - 7. Find (f o g)(x).

A) x B) x + 14 C) x - 14 D) 7

22. If f(x) = x^2 and g(x) = 1/x, find (f o g)(x).

A) x^2 B) 1/x^2 C) 1/x D) x

23. What is the value of (f o g)(1) if f(x) = x + 1 and g(x) = 2x + 1?

A) 2 B) 3 C) 4 D) 5

24. Let f(x) = cos(x) and g(x) = x^2. Find (f o g)(sqrt(pi)).

A) cos(pi) B) -1 C) cos(pi^2) D) 1

25. If f(x) = x^2 + x and g(x) = x - 1, find (f o g)(x).

A) x^2 + x - 1 B) x^2 - x C) (x - 1)^2 + (x - 1) D) x^2 - 1

26. Which of the following is true for composition of functions?

A) (f o g)(x) = (g o f)(x) always B) (f o g)(x) = f(x) * g(x) always C) (f o g)(x) = f(g(x)) D) (f o g)(x) = g(f(x)) always

27. Let f(x) = x/2 and g(x) = 2x. Find (g o f)(x).

A) x B) 2x C) x/2 D) 4x

28. If f(x) = log(x) and g(x) = 10^x, find (f o g)(x).

A) x B) log(10^x) C) 10^log(x) D) x log(10)

29. Given f(x) = x^2 and g(x) = x^2. Find (f o g)(x).

A) x^2 B) x^4 C) x^8 D) 2x^2

30. Let f(x) = 5x - 3 and g(x) = x + 2. Find (f o g)(3).

A) 10 B) 12 C) 20 D) 22

31. If f(x) = sqrt(x^2 + 1) and g(x) = x - 1, find (f o g)(2).

A) sqrt(2) B) sqrt(3) C) 2 D) sqrt(5)

32. What is the domain of (g o f)(x) if f(x) = x - 1 and g(x) = sqrt(x)?

A) x >= 0 B) x >= 1 C) x >= -1 D) All real numbers

33. Let f(x) = x^3 - 1 and g(x) = (x+1)^(1/3). Find (f o g)(x).

A) x B) x^(1/3) C) x^3 D) (x+1)

34. If f(x) = x^2 and g(x) = sin(x), find (g o f)(x).

A) sin(x^2) B) (sin(x))^2 C) sin^2(x) D) x^2 sin(x)

35. Consider f(x) = 1/x and g(x) = 1/x. Find (f o g)(x).

A) x B) 1/x C) x^2 D) 1/x^2

36. If f(x) = 2x + 3 and g(x) = x - 1, find (f o g)(5).

A) 10 B) 13 C) 16 D) 19

37. Let f(x) = ax and g(x) = bx. Find (f o g)(x).

A) abx B) a+bx C) ax+b D) (a+b)x

38. If f(x) = x^2 - 1 and g(x) = x + 1, find (g o f)(x).

A) x^2 + 2 B) x^2 + x C) x^2 D) (x+1)^2 - 1

39. What is the range of (f o g)(x) if f(x) = sqrt(x) and g(x) = x^2 for x >= 0?

A) y >= 0 B) y = 0 C) All real numbers D) y > 0

40. Let f(x) = x^2 and g(x) = x^3. Find (f o g)(x).

A) x^5 B) x^6 C) x^8 D) x^9

41. If f(x) = 2x + 1 and g(x) = (x-1)/2, find (f o g)(x).

A) x B) 2x - 1 C) (2x - 1)/2 D) x + 1

42. Consider f(x) = x - 2 and g(x) = x^2. Find (g o f)(x).

A) (x - 2)^2 B) x^2 - 2 C) x^2 - 4 D) x^2 - 4x + 4

43. If f(x) = 1/(x+1) and g(x) = x-1, find the domain of (f o g)(x).

A) x != 0 B) x != 1 C) x != -1 D) All real numbers

44. Let f(x) = tan(x) and g(x) = x + pi/2. Find (f o g)(0).

A) 0 B) 1 C) -1 D) Undefined

45. If f(x) = x^2 + 2x + 1 and g(x) = sqrt(x), find (g o f)(x).

A) x + 1 B) (x+1)^2 C) sqrt(x^2 + 2x + 1) D) x + sqrt(2x+1)

46. Given f(x) = 3x + 4 and g(x) = x - 1. What is (g o f)(2)?

A) 5 B) 6 C) 7 D) 8

47. If f(x) = x^2 and g(x) = 2x. Find (f o g)(x).

A) 2x^2 B) 4x^2 C) x^2 + 2x D) 2x

48. Let f(x) = x^2 - 1 and g(x) = x^2 + 1. Find (f o g)(x).

A) x^4 + 2x^2 B) x^4 + 1 C) x^4 D) (x^2-1)^2 + 1

49. Which of the following represents the composition of function f with itself?

A) f(x) * f(x) B) f(x) + f(x) C) f(f(x)) D) f(x) / f(x)

50. If f(x) = x and g(x) = x^2, find (f o g)(x).

A) x B) x^2 C) x^3 D) x^4

Composition of functions - Online Test

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