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Math Questions 16.4 - Composite Functions
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| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions |
|---|---|---|---|---|---|
| 16.4 | Composite Functions |
Composite Functions Revision Questions
1. . What is f(x) if g(x) = x2 and f ◦ g(x) = 2x2 - 1?
- f(x) = 2x - 1
- f(x) = x2 - 1
- f(x) = 2x2
- f(x) = x - 1
Correct Answer: A
2. . Two functions: f(x) = 1 - √x and g(x) = 3 - 2x are given. What is f ◦ g(x)?
- f ◦ g(x) = -2 - 2√x
- f ◦ g(x) = 1 - √(3 - 2x)
- f ◦ g(x) = 1 + √(3 - 2x)
- f ◦ g(x) = -2 + 2√x
Correct Answer: B
3. . Two functions: f(x) = 3/x and g(x) = 2 - x3 are given. What is g ◦ f(x)?
- g ◦ f(x) = 2 - 27/x3
- g ◦ f(x) = 2 - 3/x3
- g ◦ f(x) = 3/(2 - x3)
- g ◦ f(x) = (2 - x3)/3
Correct Answer: A
4. . Three functions: f(x) = 3x, g(x) = x2 and h(x) = 1/x are given. What is f ◦ h ◦ g (x)?
- f ◦ h ◦ g (x) = 3/x2
- f ◦ h ◦ g (x) = 3/x
- f ◦ h ◦ g (x) = 1/3x2
- f ◦ h ◦ g (x) = 3/3x
Correct Answer: A
5. . What is g ◦ f(2) if f(x) = 5x and g(x) = 1 - x2?
- -9
- -15
- -99
- 1
Correct Answer: C
6. . If f(7) = 2 and g(5) = 7, what is f ◦ g(5)?
- 2
- 5
- 7
- 14
Correct Answer: A
7. . What is 3 · f ◦ f(2) if f(x) = 2x - 1?
- 147
- 47
- 45
- 39
Correct Answer: D
8. . If f(x) = 2x2 - 5 and g(x) = x4 - 1, which of the following is true about g ◦ f(x)?
- g ◦ f(x) is not a function
- g ◦ f(x) is injective
- g ◦ f(x) is surjective
- g ◦ f(x) is a one-to-one function
Correct Answer: C
9. . The graphs of two functions, f(x) and g(x) are shown in the figure below.
What is f ◦ g(4)? - 3
- -7
- -3.5
- -2.5
Correct Answer: D
10. . The graphs of two functions, f(x) and g(x) are shown in the figure below.
What is g ◦ f (4)?
- 0
- -1
- -2
- -3
Correct Answer: B
11. . Two functions, f(x) = 2/x and g(x) = 1 - √x are given. What is the domain of f ◦ g(x)?
- D = (0, +∞)
- D = (1, +∞)
- D = (0, 1) ⋃ (1, +∞)
- D = (0, 1)
Correct Answer: C
12. . Two functions, f(x) = 4/x and g(x) = 2√x are given. What is the range of f ◦ g(x) if only the positive value of the square root is considered?
- R = (-∞, 0)
- R = (-∞, +∞)
- R = (0, +∞)
- R = [0, +∞)
Correct Answer: C
13. . Some of the values of two functions, f(x) and g(x) are shown in the following tables.
What is the value of f ◦ g(-1)? - -1
- 0
- 3
- 5
Correct Answer: D
14. . Two functions, f(x) = 2x - 5 and g(x) = x2 - 3 are given. What is f ◦ g(2) + g ◦ f(1)?
- -3
- 3
- 9
- 12
Correct Answer: B
15. . What is f ◦ f(2) - [f(3)]2 if f(x) = 3 - 2x?
- -4
- 4
- -36
- 5
Correct Answer: A
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- Check your calculations for Functions questions with our excellent Functions calculators which contain full equations and calculations clearly displayed line by line. See the Functions Calculators by iCalculator™ below.
- Continuing learning functions - read our next math tutorial: Piecewise Functions
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