[ygolo]

Originally Posted by ygolo

So I am guessing f=xf(x/y) means something else. If we were to interpret f(x/y) as "f of x/y," then what are the arguments of f on the left side of the equation? just x? If so, then what does y mean? f(x)?

Then we have f(x)=xf(x/f(x)). So f'(x)=f(x/f(x))+xf'(x/f(x))[(f(x)-xf'(x))/f^2(x)].

Another interesting thing is in this interpretation, if the problem has stated that for all f(x) satisfying, f(x)=xf(x/f(x)) the tangent line for x=0, goes through (0,0), you are essentially done also since f'(x)=f(x/f(x))+xf'(x/f(x))[(f(x)-xf'(x))/f^2(x)]=f(x/f(x)) at x=0.