TMUA 2021 Paper 1 Q5 — Worked Solution

P1·Functions, Transformations & Graphs, Algebra & Surds·6.0Official · 2021 · Q5

functional-equationmultiplicative-functionhidden-quadratic

The function

f

is such that

f (mn) = {f (m) f (n) mn if mn is a multiple of 3 if mn is not a multiple of 3

for all positive integers

m

and

n

.Given that

f (9) + f (16) - f (24) = 0

, what is the value of

f (3)

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