CAIE IGCSE Mathematics Extended E2.13.3 Composite Functions

Practise applying the inner function first, then substituting into the outer function and simplifying the result.

Syllabus
2028–2030
Objective
E2.13.3
Level
Extended

Exam points

  • read gf(x) as g(f(x)) and apply f before g
  • substitute the complete inner expression into every occurrence of the outer variable
  • simplify the composite expression before solving a composite-function equation

E2.13.3 Form composite functions as defined by gf(x) = g(f(x)) question 1

[Maximum number: 6]

10f(x)=4−3x g(x)=x2+x h(x)=3x10 \quad \mathrm{f}(x)=4-3 x \quad \mathrm{~g}(x)=x^{2}+x \quad \mathrm{~h}(x)=3^{x}

Question (a)

(a)

Find fh(2).

[ 2 ]

Question (b)

(b)

Simplify.

[ 4 ]

Question (i)

(i)

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

[ 4 ]
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