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Official 2021 Paper 1 · Q5

Paper 1Functions & graphs

The function ff is such that

f(mn)={f(m)f(n)if mn is a multiple of 3mnif mn is not a multiple of 3f(mn)=\begin{cases} f(m)f(n)&\text{if }mn\text{ is a multiple of 3}\\ mn&\text{if }mn\text{ is not a multiple of 3} \end{cases}

for all positive integers mm and nn.

Given that f(9)+f(16)−f(24)=0f(9)+f(16)-f(24)=0, what is the value of f(3)f(3)?

A83\frac83
B222\sqrt2
C33
D165\frac{16}5
E323\sqrt2
F44

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