IGCSE · Mathematics 0580 · Algebra & graphs

Functions: IGCSE Mathematics questions with answers

Free Functions questions for IGCSE Mathematics (0580), Extended tier (Supplement content), part of Algebra & graphs. Each question has the answer and the marking points an examiner would look for.

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Functions practice questions

Question 1Structured · 9 marksA* challenge

f(x) = 4x + 9x − 4, x ≠ 4.

(a)

Find f(3).

[1]
(b)

Find f⁻¹(x).

[3]
(c)

Find ff(x) in its simplest form.

[2]
(d)

Solve f(x) = x.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)−21
−21 B1
1
(b)4x + 9x − 4
y(x − 4) = 4x + 9 with x and y interchanged M1
collects x terms: x(y − 4) = 4y + 9 M1
4x + 9x − 4 A1
3
(c)x, because f is its own inverse
x B1
f⁻¹ = f, so ff(x) = ff⁻¹(x) = x (or direct simplification) B1
2
(d)x = 9 or x = −1
x2 − 8x − 9 = 0 M1
formula / completing the square M1
x = 4 ± √25 A1
3
Question 2Structured · 4 marksA* challenge

f(x) = 3x g(x) = x + 5

(a)

Find f(−2).

[1]
(b)

Solve fg(x) = 2187.

[2]
(c)

Find g−1f(x).

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)19
19 B1
1
(b)x = 2
3x + 5 = 37 M1
x = 2 A1
2
(c)3x − 5
3x − 5 B1
1
Question 3Structured · 6 marks

f(x) = 2x + 9 g(x) = x2 − 3

(a)

Find f(g(−3)).

[2]
(b)

Find f−1(x).

[2]
(c)

Find gf(x), giving your answer in the form px2 + qx + r.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)21
g(−3) = 6 M1
21 A1
2
(b)x − 92
x = 2y + 9 seen M1
x − 92 A1
2
(c)4x2 + 36x + 78
(2x + 9)2 − 3 M1
4x2 + 36x + 78 A1
2
Question 4Structured · 9 marksA* challenge

f(x) = 4x + 7x − 4, x ≠ 4.

(a)

Find f(5).

[1]
(b)

Find f⁻¹(x).

[3]
(c)

Find ff(x) in its simplest form.

[2]
(d)

Solve f(x) = x.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)27
27 B1
1
(b)4x + 7x − 4
y(x − 4) = 4x + 7 with x and y interchanged M1
collects x terms: x(y − 4) = 4y + 7 M1
4x + 7x − 4 A1
3
(c)x, because f is its own inverse
x B1
f⁻¹ = f, so ff(x) = ff⁻¹(x) = x (or direct simplification) B1
2
(d)x = 4 ± √23
x2 − 8x − 7 = 0 M1
formula / completing the square M1
x = 4 ± √23 A1
3
Question 5Structured · 4 marksA* challenge

f(x) = 2x g(x) = x + 5

(a)

Find f(−2).

[1]
(b)

Solve fg(x) = 128.

[2]
(c)

Find g−1f(x).

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)14
14 B1
1
(b)x = 2
2x + 5 = 27 M1
x = 2 A1
2
(c)2x − 5
2x − 5 B1
1
Question 6Structured · 4 marks

f(x) = 4x + 73

(a)

Solve f(x) = 13.

[2]
(b)

Find f−1(x).

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x = 8
4x + 7 = 39 M1
x = 8 A1
2
(b)3x − 74
x = 4y + 73 M1
3x − 74 A1
2

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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in