Robinson Tuition
Grade 6 · Higher · free GCSE maths worksheet

Function notation

Using f(x) and evaluating functions.

10 original questions, 31 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

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
Show answer
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
Show answer
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
Show answer
-7, -1, 2, 11
5

f(x) = 2x + 5

  1. Find f−1(x)

  2. Find f−1(11)

3 marks
Show answer
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
Show answer
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
Show answer
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
Show answer
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

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.

All Grade 6 topics