CAIE IGCSE Additional Math 1.7 Form and Use Composite Functions Questions

Practise Cambridge IGCSE Additional Mathematics by applying composition order, simplifying fg and gf expressions and solving composite-function equations.

Exam points

Form composite functions in the correct order using notation such as fg(x), gf(x) and f²(x).
Simplify composite-function expressions and evaluate them at stated inputs.
Solve equations involving composite functions while respecting the domains and order of composition.

[Maximum number: 3]

It is given that $\mathrm{f}(x)=\ln (2 x+5)$ for x>a, where a is a constant.

Using your value of a, solve the equation fg(x)=4.
Give your answers in exact form.

$\ln(2(x^2+1)+5)=4$ oe, soi
$2(x^2+1)+5=e^4$ or their $(2x^2+7)=e^4$ $x=\pm\sqrt{\frac{e^4-7}{2}}$ or exact equivalent
Alternative: solve $\ln(2x+5)=4$ to find $x=\frac{e^4-5}{2}$ , then state $g(x)=\frac{e^4-5}{2}$ .

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CAIE IGCSE Additional Math 1.7 Form and Use Composite Functions Questions question 1