Functions | CIE IGCSE Additional Maths Topic Questions 2025

1

3 marks

It is given that $h (x) = a + \frac{b}{x^{2}}$ , where $a$ and $b$ are non-zero constants.

(i)

Explain why

- 2 ⩽ x ⩽ 2

is not a suitable domain for

h (x)

.

(ii)

Given that

h (1) = 4

and

h' (1) = 16

, find the values of

a

and

b

.

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1a

1 mark

q8-0606-m20-qp-22-additional-maths

The diagram shows the graph of $f (x) = a \cos b x + c for 0 \leq x \leq \frac{8 π}{3}$ radians.

Explain why $f$ is a function.

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1b

1 mark

Write down the range of $f$ .

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1

9 marks

$f (x) = 3 e^{2 x} + 1$ for $x \in ℝ$
$g (x) = x + 1$ for $x \in ℝ$

(i)

Write down the range of

f

and the range of

g

.

(ii)

Find

g^{2} (0)

.

(iii)

Hence find

{fg}^{2} (0)

.

(iv)

On the axes below, sketch the graphs of

y = f (x)

and

y = f^{- 1} (x)

.
State the intercepts with the coordinate axes and the equations of any asymptotes.

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Functions (CIE IGCSE Additional Maths)