Free Functions questions for IGCSE Additional Mathematics (0606), part of Algebra. Each question has the answer and the marking points an examiner would look for.
Generate a full Functions worksheet →All Algebra questionsf(x) = |4x − 8|
Sketch the graph of y = f(x), stating the coordinates of the points where it meets the axes.
Solve f(x) = 4.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (2, 0) and (0, 8) V shape with vertex on x-axis B1 (2, 0) B1 (0, 8) B1 | 3 |
| (b) | x = 1, x = 3 4x − 8 = ±4 M1 x = 3 A1 x = 1 A1 | 3 |
f(x) = (x + 3)2 + 4 for x ≥ −3
State the range of f.
Find f−1(x) and state its domain.
Describe how the graphs of y = f(x) and y = f−1(x) are related.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | f(x) ≥ 4 f(x) ≥ 4 B1 | 1 |
| (b) | −3 + √(x − 4), x ≥ 4 swap x and y and rearrange M1 f−1(x) = √(x − 4) − 3 A1 domain x ≥ 4 B1 | 3 |
| (c) | reflection in y = x reflection in the line y = x B1 | 1 |
f(x) = 4x + 6 for x ∈ ℝ g(x) = 4x − 1 for x > 1
Find f−1(x).
Find the range of g.
Solve fg(x) = 22.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x − 64 correct method M1 x − 64 A1 | 2 |
| (b) | g(x) > 0 g > 0 B1 | 1 |
| (c) | x = 2 f(g(x)) = 16x − 1 + 6 M1 16x − 1 = 16 M1 x = 2 A1 | 3 |
State what is meant by the term inverse function.
State what is meant by the term one-one function.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | A function that reverses the effect of a one-one function A function that reverses the effect of a one-one function B1 | 1 |
| (b) | A function in which each value in the range comes from exactly one value in the domain A function in which each value in the range comes from exactly one value in the domain B2 | 2 |
f(x) = |3x − 6|
Sketch the graph of y = f(x), stating the coordinates of the points where it meets the axes.
Solve f(x) = 3.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (2, 0) and (0, 6) V shape with vertex on x-axis B1 (2, 0) B1 (0, 6) B1 | 3 |
| (b) | x = 1, x = 3 3x − 6 = ±3 M1 x = 3 A1 x = 1 A1 | 3 |
f(x) = (x − 1)2 + 3 for x ≥ 1
State the range of f.
Find f−1(x) and state its domain.
Describe how the graphs of y = f(x) and y = f−1(x) are related.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | f(x) ≥ 3 f(x) ≥ 3 B1 | 1 |
| (b) | 1 + √(x − 3), x ≥ 3 swap x and y and rearrange M1 f−1(x) = √(x − 3) + 1 A1 domain x ≥ 3 B1 | 3 |
| (c) | reflection in y = x reflection in the line y = x B1 | 1 |
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Meet Riyaz →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