CAIE IGCSE Additional Math 1.7 composite functions

Use this composite-functions page to substitute one function into another, simplify gh(x) or fg(x), and solve composite equations exactly.

Exam points

Form composite functions by substituting the inner function into the outer rule.
Simplify composite expressions such as gh(x) into the requested algebraic form.
Solve equations involving composite functions such as gg(x)=1 or fg(x)=5.

[Maximum number: 1]

A function g is defined by $g(x)=e^{\sqrt{x-2}}$ for $x\geqslant 2$ .

A function h is defined by $h(x)=\frac{1}{x^2}+2$ for x>0.
Find an expression for gh(x) in its simplest form.

$e^{1/x}$ or $\sqrt[x]{e}$ or $e^{x^{-1}}$
B2 Final answer
B1 for $e^{\sqrt{\frac{1}{x^2}+2-2}}$ soi oe

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