B8 Composite and inverse functions Quiz: AQA Maths, Unit 2

The 20 questions

1. Given f(x) = 2x + 3 and g(x) = x^2, find fg(x).

   • x^2 + 3
   • (2x + 3)^2
   • 2x^2 + 3
   • 2x^2 + 6

2. With f(x) = 2x + 3 and g(x) = x^2, find gf(x).

   • 4x^2 + 12x + 9
   • 2x^2 + 3
   • 4x^2 + 3
   • 2x^2 + 12x + 9

3. What is the inverse of f(x) = 2x + 3?

   • (x - 3)/2
   • (3 - x)/2
   • (x + 3)/2
   • 2x - 3

4. What is the inverse of f(x) = x^3 - 1?

   • 1/(x^3 - 1)
   • (x - 1)^(1/3)
   • x^3 + 1
   • (x + 1)^(1/3)

5. Which condition must a function satisfy to have an inverse?

   • It must be periodic
   • It must be an even function
   • It must be one-to-one
   • It must have a y-intercept

6. What is the inverse of f(x) = x^2 for x >= 0?

   • -sqrt(x)
   • 1/x^2
   • sqrt(x), for x >= 0
   • x^2, for x >= 0

7. If f(x) = 3x - 1 and g(x) = x + 2, solve fg(x) = 11.

   • x = 11/3
   • x = 3
   • x = 2
   • x = 4

8. For f(x) = 1/(x - 1) and g(x) = x + 2, what restriction applies to the domain of fg(x)?

   • x is not equal to 1
   • x is not equal to -1
   • x is not equal to 0
   • x is not equal to 2

9. The graph of f^-1 is obtained by reflecting y = f(x) in which line?

   • y = x
   • y = -x
   • The y-axis
   • The x-axis

10. For f(x) = x^2 + 1 with x >= 0, what is f^-1(10)?

    • sqrt(10)
    • 9
    • -3
    • 3

11. If f(x) = x^2 - 4 and g(x) = x + 1, find fg(x).

    • x^2 - 3
    • x^2 + 2x - 4
    • x^2 + 2x + 3
    • x^2 + 2x - 3

12. With f(x) = 2x - 1 and g(x) = x^2, for which x does f(g(x)) = g(f(x))?

    • x = 1 only
    • There are no solutions
    • x = 0 or x = 1
    • x = -1 or x = 1

13. What is the inverse of f(x) = (2x + 1)/(x - 3)?

    • (x - 3)/(2x + 1)
    • (3x - 1)/(x - 2)
    • (3x + 1)/(x - 2)
    • (3x + 1)/(2 - x)

14. What must the range of f satisfy for g(f(x)) to be defined?

    • It must lie within the domain of g
    • It must be negative
    • It must contain zero
    • It must equal the domain of f

15. If f(x) = 3x + 2, find f^-1(8).

    • 8/3
    • 10/3
    • 2
    • 6

16. If f(x) = x^2 - 2 for x >= 0 and g(x) = 2x + 1, find gf(x).

    • 4x^2 - 3
    • 2x^2 - 3
    • 2x^2 - 4x - 3
    • 2x^2 - 1

17. Why does f(x) = x^2 have no inverse over all real numbers?

    • Its range is empty
    • Its graph has no y-intercept
    • It is a linear function
    • It is not one-to-one, since f(2) = f(-2)

18. For f(x) = 4 - x and g(x) = 1/x, find fg(x).

    • 1/(4 - x)
    • 4 - 1/x
    • (4 - x)/x
    • 4 - x

19. Let f(x) = x + 1 and g(x) = 2x. Solve f(g(x)) = g(f(x)).

    • No solutions
    • All real x
    • x = 1
    • x = 0

20. If f(x) = 1/(x + 1), find ff(x) in its simplest form.

    • 1/(x + 2)
    • (x + 1)/(x + 2)
    • (x + 2)/(x + 1)
    • x + 2

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