Printable · GCSE Higher · ages 14-16
Functions, inverse and composite functions worksheet — GCSE Higher
Fifteen questions on "functions, inverse and composite functions" — DfE statement A7. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
part Higher
Functions, inverse and composite functions worksheet — GCSE Higher
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- 1.The function f(x) = x² for all real values of x has no inverse function, but g(x) = x² for x ≥ 0 does have one. Which statement correctly explains this?y = x²
- 2.f(x) = 3x − 2. Find f⁻¹(x).y = 3x − 2
- 3.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.
- 4.Ben is asked to find the inverse of f(x) = 4 − 3x. He writes f⁻¹(x) = (4 − x)/3. Which statement about Ben's answer is correct?
- 5.f(x) = x + 2 and g(x) = x². Work out the value of x for which fg(x) = gf(x).y = x + 2
- 6.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.
- 7.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.
- 8.y = 5 − 2x. Work out the value of x when y = 11.
- 9.f(x) = 2x − 1. Work out ff(x).y = 2x − 1
- 10.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.
- 11.f(x) = (x + 1)/2. Find f⁻¹(x).
- 12.f(x) = 2x² + 1 and g(x) = x − 1. Work out fg(x), giving your answer in expanded form.y = 2x² + 1
- 13.f(x) = x² − 1 and g(x) = 3x. Work out fg(4).y = x² − 1
- 14.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.
- 15.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.
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