CAIE IGCSE Mathematics Extended E2.13.3 Form Composite Functions As Defined By Gf X G F X Questions

Practise Extended CAIE IGCSE Mathematics by composing function rules, simplifying results and checking composition order.

Exam points

Form composite functions using gf(x) = g(f(x)) and related notation.
Evaluate and simplify composite functions from given function rules or mappings.
Interpret the order of composition and distinguish fg(x) from gf(x).

[Maximum number: 4]

$f(x)=3-2x\qquad g(x)=2x+3\qquad h(x)=2^x$

(a)

Find $\operatorname{gf}(-3)$ .

[ 1 ]

(b)

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

x=

[ 3 ]

$-\frac12$ oe

B2 for 4x+6+3=7 or better.
M1 for 2(2x+3)+3=7.

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