Difference between revisions of "1986 IMO Problems/Problem 5"

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(c) <math>f(x) \neq 0</math> for every <math>0 \leq x < 2</math>.
 
(c) <math>f(x) \neq 0</math> for every <math>0 \leq x < 2</math>.
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[[Category:Olympiad Algebra Problems]]
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[[Category:Functional Equation Problems]]

Revision as of 07:42, 19 July 2016

Find all (if any) functions $f$ taking the non-negative reals onto the non-negative reals, such that

(a) $f(xf(y))f(y) = f(x+y)$ for all non-negative $x$, $y$;

(b) $f(2) = 0$;

(c) $f(x) \neq 0$ for every $0 \leq x < 2$.