parmenides51 wrote: Find all functions $f:R\to R$ such that for all real $x,y$ $$f(x-f(x/y))=xf(1-f(1/y))$$... I suppose you mean (domain of functional equation) "$\forall x$, $\forall y\ne 0$" and not, as you wrote, " for all real $x,y$" Else no such function.

yes obviously, in the solution is states $y\ne 0$, I just added it

I think f(1-f(1)) is not 0 and is 0 is not possible

it means, take two cases separately

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