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20 questions and an answer page, sized for A4.

Composite and inverse functions

Year 10 · Functions & Graphs · 20 questions

Name
Date
  1. 1.
    f(x) = 6x + 2 and g(x) = 2x. Find f(g(0)).
  2. 2.
    f(x) = 5x − 4 and g(x) = 3x. Find f(g(-1)).
  3. 3.
    f(x) = 5x + 4 and g(x) = 4x. Find f(g(1)).
  4. 4.
    f(x) = 4x + 7 and g(x) = 3x. Find f(g(0)).
  5. 5.
    f(x) = 5x + 6 and g(x) = 3x. Find f(g(-2)).
  6. 6.
    f(x) = 6x + 1. Which is the inverse function f⁻¹(x)?
    a)(x − 1) / 6b)x / 6 + 1c)(x + 1) / 6d)6x − 1
  7. 7.
    f(x) = 5x + 8 and g(x) = 4x. Find f(g(0)).
  8. 8.
    f(x) = 6x + 3. Which is the inverse function f⁻¹(x)?
    a)(x − 3) / 6b)x / 6 + 3c)6x − 3d)(x + 3) / 6
  9. 9.
    f(x) = 5x + 8 and g(x) = 3x. Find f(g(-4)).
  10. 10.
    f(x) = 2x − 1 and g(x) = 4x. Find f(g(-1)).
  11. 11.
    f(x) = 4x − 1 and g(x) = 2x. Find f(g(6)).
  12. 12.
    f(x) = 4x − 3. Which is the inverse function f⁻¹(x)?
    a)x / 4 − 3b)4x + 3c)(x − 3) / 4d)(x + 3) / 4
  13. 13.
    f(x) = 6x − 2. Which is the inverse function f⁻¹(x)?
    a)x / 6 − 2b)6x + 2c)(x − 2) / 6d)(x + 2) / 6
  14. 14.
    f(x) = 6x + 0. Which is the inverse function f⁻¹(x)?
    a)x / 6 + 0b)6x − 0c)(x + 0) / 6d)(x − 0) / 6
  15. 15.
    f(x) = 2x + 0 and g(x) = 3x. Find f(g(1)).
  16. 16.
    f(x) = 5x + 0. Which is the inverse function f⁻¹(x)?
    a)(x + 0) / 5b)(x − 0) / 5c)x / 5 + 0d)5x − 0
  17. 17.
    f(x) = 6x + 5 and g(x) = 4x. Find f(g(-4)).
  18. 18.
    f(x) = 3x − 1 and g(x) = 2x. Find f(g(-1)).
  19. 19.
    f(x) = 5x − 8 and g(x) = 2x. Find f(g(1)).
  20. 20.
    f(x) = 5x − 1. Which is the inverse function f⁻¹(x)?
    a)(x + 1) / 5b)x / 5 − 1c)5x + 1d)(x − 1) / 5

Free maths worksheets and practice: rocketdigits.com/learn/composite-and-inverse-functions

Answers: Composite and inverse functions

  1. 2
  2. -19
  3. 24
  4. 7
  5. -24
  6. a) (x − 1) / 6
  7. 8
  8. a) (x − 3) / 6
  9. -52
  10. -9
  11. 47
  12. d) (x + 3) / 4
  13. d) (x + 2) / 6
  14. d) (x − 0) / 6
  15. 6
  16. b) (x − 0) / 5
  17. -91
  18. -7
  19. 2
  20. a) (x + 1) / 5

Free maths worksheets and practice: rocketdigits.com/learn/composite-and-inverse-functions

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