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.f(x) = x + 2 and g(x) = x². Work out the value of x for which fg(x) = gf(x).y = x + 2
- 2.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.
- 3.f(x) = 3x − 2. Find f⁻¹(x).y = 3x − 2
- 4.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.
- 5.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.
- 6.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.
- 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.f(x) = 2x + 1. Work out the value of x for which f⁻¹(x) = 5.y = 2x + 1
- 9.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.
- 10.f(x) = 2x − 1. Work out ff(x).y = 2x − 1
- 11.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.
- 12.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.
- 13.f(x) = (x + 1)/2. Find f⁻¹(x).
- 14.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.
- 15.f(x) = x + 3 and g(x) = 2x. Work out fg(x).y = x + 3
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