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Found problems: 2

2013 India IMO Training Camp, 1
Find all functions $f$ from the set of real numbers to itself satisfying \[ f(x(1+y)) = f(x)(1 + f(y)) \] for all real numbers $x, y$.
cauchy equation limit function induction algebra Cauchy-Schwarz inequality functional equations limits mathematical induction

2013 India IMO Training Camp, 1
Find all functions $f$ from the set of real numbers to itself satisfying \[ f(x(1+y)) = f(x)(1 + f(y)) \] for all real numbers $x, y$.
cauchy equation limit function induction algebra Cauchy-Schwarz inequality functional equations limits mathematical induction