JEE Main - Real-valued functions and algebra of functions Online Test (MCQ Quiz)

1. What is the domain of the function f(x) = sqrt(x^2 - 4)?

A) (-inf, -2] U [2, inf) B) (-2, 2) C) (-inf, inf) D) (-2, inf)

2. What is the range of the function f(x) = x^2 + 1?

A) [0, inf) B) [1, inf) C) (-inf, 1] D) (1, inf)

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

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

4. If f(x) = x - 1 and g(x) = x^2, what is (f*g)(x)?

A) (x-1)x^2 B) x^2 - x C) x^3 - x^2 D) x^2(x-1)

5. If f(x) = 2x and g(x) = x + 3, what is (f/g)(x)?

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

6. What is the domain of f(x) = 1/x?

A) All real numbers B) All real numbers except 0 C) All positive real numbers D) All negative real numbers

7. What is the range of f(x) = |x|?

A) All real numbers B) All positive real numbers C) All non-negative real numbers D) All integers

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

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

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

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

10. What is the domain of f(x) = ln(x)?

A) All real numbers B) All positive real numbers C) All non-negative real numbers D) All real numbers except 0

11. What is the range of f(x) = e^x?

A) All real numbers B) All positive real numbers C) All non-negative real numbers D) (0, inf)

12. If f(x) = sqrt(x) and g(x) = x^2, what is the domain of (f o g)(x)?

A) All real numbers B) All non-negative real numbers C) All positive real numbers D) (-inf, 0]

13. If f(x) = x^2 and g(x) = sqrt(x), what is the domain of (g o f)(x)?

A) All real numbers B) All non-negative real numbers C) All positive real numbers D) (-inf, 0]

14. What is the domain of f(x) = tan(x)?

A) All real numbers B) All real numbers except n*pi, where n is an integer C) All real numbers except (n + 1/2)*pi, where n is an integer D) All real numbers except n*pi/2, where n is an integer

15. What is the range of f(x) = sin(x)?

A) [0, 1] B) (-1, 1) C) [-1, 1] D) (-inf, inf)

16. If f(x) = c (a constant function), what is its domain?

A) All positive real numbers B) All non-negative real numbers C) All real numbers D) The set {c}

17. If f(x) = c (a constant function), what is its range?

A) All real numbers B) All positive real numbers C) The set {c} D) The empty set

18. Which of the following is NOT a real-valued function?

A) f(x) = x^2 B) f(x) = sqrt(x) C) f(x) = 1/x D) f(x) = sqrt(-x)

19. If f(x) = x and g(x) = x, then (f-g)(x) is:

A) x B) 0 C) 2x D) 1

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

A) 5 B) 6 C) f(x)+g(x) D) 2+3

21. If f(x) = x+1 and g(x) = 1/(x+1), what is the domain of (f*g)(x)?

A) All real numbers B) All real numbers except -1 C) All positive real numbers D) (-1, inf)

22. If f(x) = x^2 and g(x) = x-1, what is the domain of (f/g)(x)?

A) All real numbers B) All real numbers except 1 C) All non-negative real numbers D) [0, 1)

23. What is the domain of f(x) = arcsin(x)?

A) (-inf, inf) B) [0, 1] C) [-1, 1] D) (0, 1)

24. What is the range of f(x) = arccos(x)?

A) [0, pi] B) [0, 1] C) [-1, 1] D) (0, pi)

25. If f(x) = x^3, what is f^-1(x)?

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

26. A function f is defined by f(x) = sqrt(1-x^2). What is its domain?

A) (-inf, 1] B) [1, inf) C) [-1, 1] D) (0, 1)

27. A function f is defined by f(x) = sqrt(1-x^2). What is its range?

A) (-inf, 1] B) [1, inf) C) [0, 1] D) (0, 1)

28. If f(x) = x^2 - 1 and g(x) = x+1, what is the domain of (f/g)(x)?

A) All real numbers B) All real numbers except -1 C) All real numbers except 1 D) (-inf, -1)

29. If f(x) = x-1 and g(x) = x+1, what is (f o g)(x)?

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

30. If f(x) = x+1 and g(x) = x-1, what is (g o f)(x)?

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

31. What is the domain of f(x) = 1/sqrt(x-2)?

A) (2, inf) B) [2, inf) C) (-inf, 2) D) (-inf, 2]

32. What is the range of f(x) = 2^x?

A) All real numbers B) All positive real numbers C) All non-negative real numbers D) (0, inf)

33. If f(x) = 3x - 2, what is f^-1(x)?

A) (x+2)/3 B) (x-2)/3 C) 1/(3x-2) D) 3x+2

34. Let f(x) = x^2 + 1. Which of the following is NOT in the range of f?

A) 1 B) 2 C) 0 D) 5

35. If f(x) = sqrt(x-a) and g(x) = x^2, what is the domain of (f o g)(x)?

A) All real numbers B) All real numbers such that x^2 >= a C) All non-negative real numbers D) All real numbers except sqrt(a)

36. If f(x) = x^2 and g(x) = sqrt(x-a), what is the domain of (g o f)(x)?

A) All real numbers B) All real numbers such that x^2 >= a C) All non-negative real numbers D) All real numbers except sqrt(a)

37. What is the domain of f(x) = log_a(x) where a > 0 and a != 1?

A) All real numbers B) All positive real numbers C) All non-negative real numbers D) All real numbers except 0

38. What is the range of f(x) = log_a(x) where a > 0 and a != 1?

A) All positive real numbers B) All non-negative real numbers C) All real numbers D) (-inf, 0)

39. If f(x) = x and g(x) = x, then (f/g)(x) is defined for:

A) All real numbers B) All real numbers except 0 C) All positive real numbers D) All non-zero real numbers

40. If f(x) = 0, what is its range?

A) All real numbers B) The set {0} C) The empty set D) Positive real numbers

41. Let f(x) = sqrt(4-x^2). What is the domain of f?

A) (-inf, 2] B) [2, inf) C) [-2, 2] D) (0, 2)

42. Let f(x) = sqrt(4-x^2). What is the range of f?

A) (-inf, 2] B) [2, inf) C) [0, 2] D) (0, 2)

43. If f(x) = x^2 and g(x) = 1/x, what is the domain of (g o f)(x)?

A) All real numbers B) All real numbers except 0 C) All positive real numbers D) All non-negative real numbers

44. If f(x) = 1/x and g(x) = x^2, what is the domain of (g o f)(x)?

A) All real numbers B) All real numbers except 0 C) All positive real numbers D) All non-negative real numbers

45. If f(x) = x+1 and g(x) = x-1, what is the domain of (f/g)(x)?

A) All real numbers B) All real numbers except 1 C) All real numbers except -1 D) (-inf, 1)

46. If f(x) = x-1 and g(x) = x+1, what is the domain of (f/g)(x)?

A) All real numbers B) All real numbers except 1 C) All real numbers except -1 D) (-inf, -1)

47. What is the domain of f(x) = sqrt(x^2 - 9)?

A) (-inf, -3] U [3, inf) B) (-3, 3) C) (-inf, inf) D) (-3, inf)

48. What is the range of f(x) = -x^2?

A) [0, inf) B) (-inf, 0] C) (-inf, inf) D) (0, inf)

49. If f(x) = x^2 and g(x) = x^2, what is (f-g)(x)?

A) 0 B) x^4 C) 2x^2 D) 1

50. If f(x) = x and g(x) = c (constant), what is (f+g)(x)?

A) cx B) x+c C) xc D) c

Real-valued functions and algebra of functions - Online Test

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