Robinson Tuition
Grade 6 · Higher · free GCSE maths worksheet

Function notation

Using f(x) and evaluating functions.

10 original questions, 31 marks. Type your answers below for an instant mark and a score, or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

f(x) = 2x + 3

Work out

  1. f(4)
  2. f(−2)
2 marks
Show answer
a) 11 b) -1
2

f(x) = 3x − 4    g(x) = x2

  1. Find f(5)

  2. Find gf(2)

3 marks
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a) 11 b) 4
3

g(x) = x2 − 5

  1. Work out g(3).
  2. Work out g(−4).
  3. Find the two values of x for which g(x) = 20.
3 marks
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a) 4 b) 11 c) x = 5 or x = -5
4

f(x) = 3x − 1

Complete the table of values.

x−2014
f(x)
2 marks
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-7, -1, 2, 11
5

f(x) = 2x + 5

  1. Find f−1(x)

  2. Find f−1(11)

3 marks
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a) f-1(x) = (x - 5)/2 b) 3
6

f(x) = 4x + 9

  1. Solve f(x) = −7.
  2. Solve f(x) = x.
4 marks
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a) x = -4 b) x = -3
7

f(x) = 2x − 13

  1. The output of the function is 5. Find the input.
  2. The output of the function is −3. Find the input.
3 marks
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a) x = 8 b) x = -4
8

f(x) = x2 + 2x

Express f(x + 3) in the form x2 + bx + c where b and c are integers.

3 marks
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x2 + 8x + 15
9

f(x) = x2 + 2x

  1. Work out f(3) + f(−1).
  2. Write f(2x) in terms of x. Give your answer in its simplest form.
4 marks
Show answer
a) 14 b) 4x2 + 4x
10

f(x) = 3x − 4

  1. Show that f(x + 2) − f(x) = 6 for every value of x.
  2. Solve f(2x) = f(x + 5).
4 marks
Show answer
a) Shown: the difference is 6 b) x = 5

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Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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