Printable · GCSE Foundation · ages 14-16

Functions, inverse and composite functions worksheet — GCSE Foundation

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.

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Functions, inverse and composite functions worksheet — GCSE Foundation

Maths · GCSE Foundation · A7 · Functions, inverse and composite functions · 15 questions

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1.y = 5 − 2x. Work out the value of x when y = 11.
(a)8
(b)3
(c)6
(d)−3
2.y = x + 10. Work out the value of y when x = 0.
y = x + 10
(a)0
(b)10
(c)11
(d)−10
3.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.
(a)19
(b)21
(c)22
(d)16
4.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.
(a)£165
(b)£105
(c)£75
(d)£90
5.A number machine adds 5 to its input. Work out the output when the input is 0.
(a)5
(b)−5
(c)0
(d)6
6.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.
(a)y = x − 1
(b)y = 2x − 1
(c)y = 3x − 1
(d)y = 2x + 1
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.
(a)£13.20
(b)£15.50
(c)£34.20
(d)£16.70
8.y = x + 4. Work out the value of y when x = 3.
y = x + 4
(a)7
(b)1
(c)12
(d)4
9.A number machine adds 6 to its input. Work out the output when the input is −4.
(a)10
(b)−10
(c)2
(d)−24
10.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.
(a)7
(b)17
(c)12
(d)2
11.A number machine multiplies its input by 5. Work out the output when the input is −1.
(a)−5
(b)5
(c)4
(d)−6
12.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.
(a)2
(b)−18
(c)−6
(d)−2
13.y = 5x − 1. Work out the value of y when x = 3.
y = 5x − 1
(a)14
(b)16
(c)15
(d)10
14.A number machine multiplies its input by 3. The output is 15. Work out the input.
(a)45
(b)12
(c)18
(d)5
15.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.
(a)y = 3x − 2
(b)y = x + 4
(c)y = 3x + 2
(d)y = 2x + 3

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