ConceptConceptDocsDocuments

CAIE IGCSE Additional Math 1 functions

Use this Functions hub to move from terminology and notation into domains, ranges, inverse functions, composite functions and graph sketches.

Syllabus
2028–2030
Course
Additional Mathematics 0606

Covered syllabus points

1.1. Understand function terminology1.2. Find domains and ranges of functions1.3. Use function notation1.4. Relate y = f(x) and y = |f(x)|1.5. Explain when inverses do not exist1.6. Find inverse functions1.7. Form and use composite functions1.8. Sketch functions and inverses

1. Functions question 1

[Maximum number: 2]
Figure for Question 1. Functions question 1 — CAIE IGCSE Additional Math

The diagram shows the graph of f(x)=acos⁡bx+cf(x)=a\cos bx+c, for 0⩽x⩽8π30\leqslant x\leqslant\frac{8\pi}{3} radians.

Question (a)

(a)

Explain why f is a function.

[ 1 ]

Question (b)

(b)

Write down the range of f.

[ 1 ]

1. Functions question 2

[Maximum number: 9]

Question (a)

(a)

Describe the relationship between the graph of f(x) and the graph of f−1(x)f^{-1}(x).

[ 1 ]

Question (b)

(b)

A function g is defined by g(x)=ex−2g(x)=e^{\sqrt{x-2}} for x⩾2x\geqslant 2.

[ 8 ]

Question (i)

(i)

Find an expression for g−1(x)g^{-1}(x).

[ 4 ]

Question (ii)

(ii)

Write down the range of g−1g^{-1}.

[ 3 ]

Question (iii)

(iii)

A function h is defined by h(x)=1x2+2h(x)=\frac{1}{x^2}+2 for x>0.
Find an expression for gh(x) in its simplest form.

[ 1 ]

1. Functions question 3

[Maximum number: 10]

Question (a)

(a)
Table for Question (a) — CAIE IGCSE Additional Math
[ 5 ]

Question (b)

(b)

It is given that h(x)=(x−1)2+3h(x)=(x-1)^2+3 for x⩾ax\geqslant a. The value of a is as small as possible such that h−1h^{-1} exists.

[ 5 ]

Question (i)

(i)

Write down the value of a.

[ 1 ]

Question (ii)

(ii)

Write down the range of h.

[ 1 ]

Question (iii)

(iii)

Find h−1(x)h^{-1}(x) and state its domain.

[ 3 ]
All question bank results loaded