EduNinja

[Maximum number: 10]

$10 \quad \mathrm{f}(x)=4-3 x \quad \mathrm{~g}(x)=x^{2}+x \quad \mathrm{~h}(x)=3^{x}$

(a)

Find fh(2).

[ 2 ]

23
M1 for $4-3(3^2)$ oe soi.

(b)

Find $f^{-1}(x)$ .

$f^{-1}(x)=$

[ 2 ]

$\frac{4-x}{3}$ oe final answer.
M1 for x=4-3y, y+3x=4, x+3y=4, $\frac{y}{-3}=\frac{4}{-3}+x$ oe, or $\frac{x}{-3}=\frac{4}{-3}+y$ oe.

(c)

Simplify.

[ 6 ]

(i)

f(1-2 x)

[ 2 ]

(ii)

$\operatorname{gf}(x)-9 \mathrm{~g}(x)$

[ 4 ]

20-36x or 4(5-9x) final answer.
B3 for 20-36x seen in working then spoiled.
OR M1 for $(4-3x)^2+4-3x-9(x^2+x)$ or better.
B1 for $(4-3x)^2=16-12x-12x+9x^2$ or better.
B1 for answer 20-kx or k-36x oe, or answer 20-36x with one sign/term error in working.

CAIE IGCSE Mathematics Extended E2.13 Functions Topic Practice

Question 1

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)