Composition of functions - Question Bank

1. Let f(x) = 1/(x-2) and g(x) = x^2. Find the domain of (f o g)(x).
A) x != sqrt(2) and x != -sqrt(2)
B) x != 2
C) All real numbers
D) x != 0
2. 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
3. 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)
4. 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
5. 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
6. Given f(x) = 3x + 4 and g(x) = x - 1. What is (g o f)(2)?
A) 5
B) 6
C) 7
D) 8
7. 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)
8. Let f(x) = tan(x) and g(x) = x + pi/2. Find (f o g)(0).
A) 0
B) 1
C) -1
D) Undefined
9. 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
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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
16. If f(x) = 2x + 3 and g(x) = x - 1, find (f o g)(5).
A) 10
B) 13
C) 16
D) 19
17. 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
18. 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)
19. 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)
20. 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
21. 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)
22. Let f(x) = 5x - 3 and g(x) = x + 2. Find (f o g)(3).
A) 10
B) 12
C) 20
D) 22
23. 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
24. 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)
25. Let f(x) = x/2 and g(x) = 2x. Find (g o f)(x).
A) x
B) 2x
C) x/2
D) 4x
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. 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
28. 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
29. 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
30. 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
31. 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
32. If f(x) = 2x and g(x) = 3x, what is (f o g)(x)?
A) 5x
B) 6x
C) 2x + 3x
D) x
33. 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)
34. 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
35. 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
36. 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
37. 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
38. Let f(x) = 2x + 1 and g(x) = x^2 - 1. Find (g o f)(2).
A) 15
B) 24
C) 48
D) 16
39. 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
40. 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|
41. 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
42. 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
43. 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
44. 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))
45. If f(x) = 2x and g(x) = x/2, what is (f o g)(x)?
A) x
B) 2x
C) x/2
D) 4x
46. 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)
47. 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
48. 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
49. 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)
50. 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
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