CAIE IGCSE Mathematics Extended E2.13 Functions Topic Practice

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Covered syllabus points

E2.13.1 Understand functions, domain and range and use function notation.E2.13.2 Understand and find inverse functions f –1(x).E2.13.3 Form composite functions as defined by gf(x) = g(f(x))

Question 1

[Maximum number: 2]

4 f(x)=3x-5
The domain of f(x) is {−3,0,2}\{-3,0,2\}.
Find the range of f(x).

Question 2

[Maximum number: 9]

f(x)=3−2xg(x)=2x+3h(x)=2xf(x)=3-2x\qquad g(x)=2x+3\qquad h(x)=2^x

Question (a)

(a)

Find f(-3).

[ 1 ]

Question (b)

(b)

Find gf⁡(−3)\operatorname{gf}(-3).

[ 1 ]

Question (c)

(c)

Find f−1(x)\mathrm{f}^{-1}(x).

f−1(x)=\mathrm{f}^{-1}(x)=
[ 2 ]

Question (d)

(d)

Find x when gg⁡(x)=7\operatorname{gg}(x)=7.

x=
[ 3 ]

Question (e)

(e)

Find x when h−1(x)=5\mathrm{h}^{-1}(x)=5.

x=
[ 2 ]
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