CAIE IGCSE Mathematics Extended E2.13 Functions

Covered syllabus points

[Maximum number: 2]

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

[Maximum number: 8]

\mathrm{f}(x)=5^{x} \quad \mathrm{~g}(x)=3 x-2 \quad \mathrm{~h}(x)=x^{2}+1

(a)

Find f(5).

[ 1 ]

(b)

Find g(8 x).

[ 1 ]

(c)

Find $\mathrm{g}^{-1}(x)$ .

\mathrm{g}^{-1}(x)=

[ 2 ]

$\frac{x+2}{3}$ or $\frac{x}{3}+\frac{2}{3}$ final answer

M1 for correct first step
e.g. x=3 y-2 or y+2=3 x or $\frac{y}{3}=x-\frac{2}{3}$
oe

(d)

Find the positive solution of gh(x)=364.

[ 3 ]

11

M2 for $3 x^{2}+1=364$ or better or M1 for $3\left(x^{2}+1\right)-2$

Alternative method:

M2 for $x^{2}+1=(364+2) \div 3$ or M1 for 3 x-2=364

(e)

Find $\mathrm{ff}^{-1}(12)$ .

[ 1 ]

[Maximum number: 3]

\mathrm{f}(x)=5^{x} \quad \mathrm{~g}(x)=3 x-2 \quad \mathrm{~h}(x)=x^{2}+1

Find the positive solution of gh(x)=364.

11

M2 for $3 x^{2}+1=364$ or better or M1 for $3\left(x^{2}+1\right)-2$

Alternative method:

M2 for $x^{2}+1=(364+2) \div 3$ or M1 for 3 x-2=364

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