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Edexcel IGCSE Maths

Topic questions Pure mathematics Functions, domain & range

Functions, domain & range

6 questions · 66 marks · about 1.5 hours

Functions, domain and range questions

TopicFunctions, domain & range

Edexcel 4MB1 Functions, domain and range 6 questions

Paper 1 June 2025 (R), Question 26 8 marks

Question 26, shown as an image
(a)

Find gmaths symbolmaths symbol2maths symbol

[1]
Reveal mark scheme Mark scheme for question 26(a)
(b)

Find the range of g

[2]
Reveal mark scheme Mark scheme for question 26(b)
(c)

Express the inverse function gmaths symbol1 in the form gmaths symbol1: x maths symbol...

gmaths symbol1: x maths symbol........

Question 26, shown as an image
[3]
Reveal mark scheme Mark scheme for question 26(c)
(d)

Express the composite function gh in the form gh: x maths symbol fraction where a, b and c are integers.

gh: x maths symbol........

[2]
Reveal mark scheme Mark scheme for question 26(d)

Paper 2 June 2024 (R), Question 10 14 marks

f and g are two functions such that

f: x maths symbol x2 + 2x where x maths symbol

(a)

State the value of x that must be excluded from any domain of g

[1]
Reveal mark scheme Mark scheme for question 10(a)
(b)

Find f(3)

[1]
Reveal mark scheme Mark scheme for question 10(b)
(c)

Find the value of x for which g(x) = 5

[2]
Reveal mark scheme Mark scheme for question 10(c)
(d)

Find fg(24)

[2]
Reveal mark scheme Mark scheme for question 10(d)
(e)

Find the value of x for which gf(x) = 4

Show your working clearly.

[4]
Reveal mark scheme Mark scheme for question 10(e)
(f)

The function h is such that h: x maths symbol 5x2 maths symbol 10x maths symbol 4 where x maths symbol 1

Find the inverse of h(x) in the form hmaths symbol1: x maths symbol...

Question 10, shown as an image
[4]
Reveal mark scheme Mark scheme for question 10(f)

Paper 2 June 2023 (R), Question 8 13 marks

The function f is such that

Question 8, shown as an image
(a)

State a value that cannot be in the range of the function f

[1]
Reveal mark scheme Mark scheme for question 8(a)
(b)

Solve 16 f(x) = x + 8

[4]
Reveal mark scheme Mark scheme for question 8(b)
(c)

Show that ff(x) = f–1(x)

[6]
Reveal mark scheme Mark scheme for question 8(c)
(d)

State a value that cannot be in the domain of the function f–1

[1]
Reveal mark scheme Mark scheme for question 8(d)
(e)

Evaluate fff(2)

Question 8, shown as an image
[1]
Reveal mark scheme Mark scheme for question 8(e)

Paper 2 January 2023 (R), Question 7 10 marks

The function g is defined as

Question 7, shown as an image
(a)

Find the value of x that must be excluded from the domain of g

[1]
Reveal mark scheme Mark scheme for question 7(a)
(b)

Solve g(x) = 5

[3]
Reveal mark scheme Mark scheme for question 7(b)
(c)

The function f is defined as

Question 7, shown as an image
[2]
Reveal mark scheme Mark scheme for question 7(c)
(d)

Express the inverse function f–1 in the form f–1:x maths symbol...

Question 7, shown as an image
[4]
Reveal mark scheme Mark scheme for question 7(d)

Paper 2 January 2023, Question 12 15 marks

Also involves Completing the square

Figure for question 12
(a)

State the value of x that must be excluded from any domain of g

[1]
Reveal mark scheme Mark scheme for question 12(a)
(b)

Find the value of k such that g(k) = 8

[3]
Reveal mark scheme Mark scheme for question 12(b)
(c)

Find fg(−3)

[2]
Reveal mark scheme Mark scheme for question 12(c)
(d)
Question 12, shown as an image
Question 12, shown as an image
[4]
Reveal mark scheme Mark scheme for question 12(d)
(e)

The function h is defined for all values of x as

Figure for question 12

where a and b are constants.

Given that

h(2) = 4

Figure for question 12

find the value of a and the value of b

Show clear algebraic working.

[5]
Reveal mark scheme Mark scheme for question 12(e)

Paper 1 January 2019, Question 24 6 marks

Question 24, shown as an image
(a)

Find f (2)

[1]
Reveal mark scheme Mark scheme for question 24(a)
(b)

Find the range of f.

[1]
Reveal mark scheme Mark scheme for question 24(b)
(c)

Express the inverse function f–1 in the form f–1:x maths symbol...

[3]
Reveal mark scheme Mark scheme for question 24(c)
(d)

The function g is defined by g:x maths symbol 4x – 5

Express the composite function fg in the form fg(x) =...

[1]
Reveal mark scheme Mark scheme for question 24(d)

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