JEE Main - Inverse functions and graphs of simple functions Online Test (MCQ Quiz)

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

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

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

A) [0, π] B) (-π/2, π/2) C) [0, π/2] D) (-∞, ∞)

3. The function f(x) = arctan(x) is defined for all real numbers. What is its range?

A) [0, π] B) (-π/2, π/2) C) [0, π/2] D) (-∞, ∞)

4. What is the principal value range of the inverse trigonometric function arccot(x)?

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

5. If f(x) = 2^x, what is its inverse function, f⁻¹(x)?

A) -2^x B) log₂(x) C) x/2 D) log₁₀(x)

6. What is the domain of the inverse function of f(x) = e^x?

A) (-∞, ∞) B) (0, ∞) C) [0, ∞) D) (-1, 1)

7. The graph of y = x³ is symmetric with respect to:

A) The x-axis B) The y-axis C) The origin D) The line y = x

8. If f(x) = 1/x, what is its inverse function, f⁻¹(x)?

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

9. The graph of y = |x| has a minimum value at:

A) x = -1 B) x = 1 C) x = 0 D) All x

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

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

11. The range of the function f(x) = sin(x) is:

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

12. What is the domain of the function f(x) = log_b(x) where b > 1?

A) (-∞, ∞) B) [0, ∞) C) (0, ∞) D) (-∞, 0)

13. The graph of y = x² is symmetric with respect to:

A) The x-axis B) The y-axis C) The origin D) The line y = -x

14. Which of the following is NOT an odd function?

A) f(x) = x³ B) f(x) = sin(x) C) f(x) = x D) f(x) = x²

15. Which of the following is NOT an even function?

A) f(x) = x² B) f(x) = cos(x) C) f(x) = |x| D) f(x) = x³

16. What is the value of arcsin(1/2)?

A) π/6 B) π/4 C) π/3 D) π/2

17. What is the value of arccos(0)?

A) 0 B) π/4 C) π/2 D) π

18. What is the value of arctan(1)?

A) 0 B) π/4 C) π/3 D) π/2

19. If f(x) = log_b(x), its inverse function f⁻¹(x) is:

A) b^x B) x^b C) log_x(b) D) 1/log_b(x)

20. The graph of y = c (where c is a constant) is a:

A) Vertical line B) Horizontal line C) Parabola D) Hyperbola

21. What is the domain of f(x) = cot(x)?

A) (-∞, ∞) B) R - {nπ | n ∈ Z} C) R - {(2n+1)π/2 | n ∈ Z} D) (0, π)

22. What is the range of f(x) = sec(x)?

A) (-1, 1) B) [-1, 1] C) (-∞, -1] ∪ [1, ∞) D) [1, ∞)

23. The graph of y = 1/x² is symmetric with respect to:

A) The x-axis B) The y-axis C) The origin D) The line y = x

24. What is the principal value range of arcsec(x)?

A) [0, π] - {π/2} B) [0, π/2] ∪ [π/2, π] C) [0, π] D) (-π/2, π/2) - {0}

25. What is the principal value range of arccsc(x)?

A) [-π/2, 0) ∪ (0, π/2] B) [0, π] - {0} C) (-π/2, π/2) - {0} D) [0, π]

26. If f(x) = a^x where a > 0 and a ≠ 1, its inverse function f⁻¹(x) is:

A) log_a(x) B) log_x(a) C) x^a D) a/x

27. The graph of y = √(-x) is a reflection of the graph of y = √x across:

A) The x-axis B) The y-axis C) The origin D) The line y = x

28. What is the domain of the function f(x) = log(x²)?

A) (-∞, ∞) B) [0, ∞) C) (0, ∞) D) R - {0}

29. The graph of y = -x³ is symmetric with respect to:

A) The x-axis B) The y-axis C) The origin D) The line y = x

30. What is the value of arcsin(-1/2)?

A) π/6 B) -π/6 C) π/3 D) -π/3

31. What is the value of arccos(-1)?

A) 0 B) π/2 C) π D) 3π/2

32. What is the value of arctan(-√3)?

A) π/3 B) -π/3 C) π/6 D) -π/6

33. The graph of y = 1/x is symmetric with respect to:

A) The x-axis B) The y-axis C) The origin D) The line y = x and the origin

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

A) (-∞, ∞) B) R - {nπ | n ∈ Z} C) R - {(2n+1)π/2 | n ∈ Z} D) (-π/2, π/2)

35. What is the range of f(x) = csc(x)?

A) (-1, 1) B) [-1, 1] C) (-∞, -1] ∪ [1, ∞) D) [1, ∞)

36. If f(x) = x, what is f⁻¹(x)?

A) -x B) 1/x C) x D) 0

37. The graph of y = x^n for odd integer n > 1 is similar to the graph of:

A) y = x² B) y = x³ C) y = |x| D) y = 1/x

38. The graph of y = x^n for even integer n > 1 is similar to the graph of:

A) y = x³ B) y = x² C) y = x D) y = 1/x

39. What is the domain of f(x) = arcsin(2x)?

A) (-∞, ∞) B) [-1, 1] C) [-1/2, 1/2] D) (0, 1)

40. What is the range of f(x) = 3 + arctan(x)?

A) [3, 3+π] B) (3-π/2, 3+π/2) C) [0, π] D) (-∞, ∞)

41. The graph of y = ln(x) is the reflection of y = e^x across:

A) The x-axis B) The y-axis C) The origin D) The line y = x

42. What is the value of arccot(-1)?

A) π/4 B) 3π/4 C) 5π/4 D) -π/4

43. The function f(x) = x|x| is:

A) Even B) Odd C) Neither even nor odd D) Both even and odd

44. The graph of y = 1/(x-a) is a translation of y = 1/x by 'a' units in the:

A) Positive y-direction B) Negative y-direction C) Positive x-direction D) Negative x-direction

45. What is the domain of the inverse function of f(x) = log₂(x)?

A) (-∞, ∞) B) (0, ∞) C) [0, ∞) D) (-1, 1)

46. Which function's graph passes through the origin?

A) f(x) = 1/x B) f(x) = e^x C) f(x) = x³ D) f(x) = log(x)

47. The graph of y = x² - 1 is a translation of y = x² by:

A) 1 unit up B) 1 unit down C) 1 unit left D) 1 unit right

48. What is the range of the function f(x) = arcsin(x) + arccos(x)?

A) [0, π] B) [0, π/2] C) [π/2, π] D) {π/2}

49. The graph of y = tan⁻¹(x) has horizontal asymptotes at:

A) y = 0 and y = π B) y = -π/2 and y = π/2 C) y = -π and y = π D) y = 1 and y = -1

50. If f(x) = x + 1, what is f⁻¹(x)?

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

Inverse functions and graphs of simple functions - Online Test

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