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2019 MMATHS Tiebreaker p4 - c^2f(x + y) = f(x)f(y), continuous f

Source:

October 7, 2023

functional equationalgebra

Problem Statement

The continuous function

f(x)

satisfies

c^2f(x + y) = f(x)f(y)

for all real numbers

x

and

y,

where

c > 0

is a constant. If

f(1) = c

, find

f(x)

(with proof).