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Found problems: 2

2013 Dutch BxMO/EGMO TST, 4
Tags: functional equation , determine all functions , algebra
Determine all functions $f:\mathbb{R}\to\mathbb{R}$ satisfying \[f(x+yf(x))=f(xf(y))-x+f(y+f(x))\]

2013 Dutch BxMO/EGMO TST, 4
Tags: algebra , functional equation , determine all functions
Determine all functions $f:\mathbb{R}\to\mathbb{R}$ satisfying \[f(x+yf(x))=f(xf(y))-x+f(y+f(x))\]