2.5 Inverse functions Quiz: AQA Further Maths, Unit 2

The 20 questions

1. For f(x) = 2x + 3, which expression is f^(−1)(x)?

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

2. For f(x) = 5x, which expression is f^(−1)(x)?

   • 5/x
   • −5x
   • x − 5
   • x/5

3. What does f^(−1)(f(x)) simplify to?

   • 0
   • 1
   • x
   • f(x)

4. For f(x) = 2x + 3, what is f^(−1)(7)?

   • 5
   • 4
   • 2
   • 10

5. What property must a function have for its inverse to be a function?

   • Many-to-many
   • Many-to-one
   • One-to-many
   • One-to-one

6. What is the inverse of f(x) = x^3?

   • ∛x
   • 1/x^3
   • 3x
   • x^3

7. For f(x) = (x + 2)/3, what is f^(−1)(x)?

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

8. For f(x) = x^2 + 1 with x ≥ 0, what is f^(−1)(x)?

   • x − 1
   • √(x + 1)
   • √(x − 1)
   • (x − 1)^2

9. For f(x) = 1/(x − 4), what is f^(−1)(x)?

   • 1/(x + 4)
   • 1/x − 4
   • x + 4
   • 1/x + 4

10. If f^(−1)(x) = (x + 5)/4, what is f^(−1)(3)?

    • 4
    • 8
    • 2
    • 1.25

11. For f(x) = 3 − 2x, what is f^(−1)(x)?

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

12. For f(x) = 2x and g(x) = x + 1, what is f^(−1)(g(3))?

    • 1
    • 2
    • 8
    • 4

13. For f(x) = 4x − 8, what value of x satisfies f^(−1)(x) = x?

    • 8/3
    • 2
    • 8
    • −8/3

14. The graph of an inverse function is a reflection of the graph of the original function in which line?

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

15. For f(x) = (2x − 1)/(x + 3), what is f^(−1)(x)?

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

16. For f(x) = x^2 − 4 with x ≥ 0, what is f^(−1)(5)?

    • 3
    • 9
    • 21
    • 1

17. Let f(x) = x + 2 and g(x) = 2x. What is (fg)^(−1)(x)?

    • (x − 2)/2
    • (x + 2)/2
    • 2x − 2
    • x/2 + 2

18. For f(x) = x^3 − 2, what is f^(−1)(6)?

    • 2
    • 4
    • −2
    • 8

19. For f(x) = 3x + k, f^(−1)(7) = 2. What is k?

    • 2
    • 13
    • 1
    • −1

20. For f(x) = √(x + 1) with x ≥ −1, what is the domain of f^(−1)?

    • x ≥ −1
    • x ≥ 1
    • All real numbers
    • x ≥ 0

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