Edexcel IGCSE Math A 3.2.HD inverse and composite functions

Practise function-composition questions by substituting one rule into another, rearranging for inverses and respecting any domain restriction.

Exam points

Find composite functions such as gf(x) by substituting one function rule into another.
Rearrange y = f(x) to write the inverse function f⁻¹(x) in correct notation.
Use stated restrictions such as x ≤ 2 when choosing the correct inverse branch.

[Maximum number: 2]

f is the function such that f(x)=4-3 x

Work out fg(-1.5)

$g(-1.5)=\frac{1}{1-2(-1.5)}=\frac14=0.25$ f(g(-1.5))=4-3(0.25)=3.25

Final answer:
3.25

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