Y by v4913, MathLuis, fluff_E, HWenslawski, megarnie, son7, GoodMorning, michaelwenquan, jk2845, aidan0626
Let
be the set of all positive real numbers. Find all functions
such that for all
we have
![\[f(x) = f(f(f(x)) + y) + f(xf(y)) f(x+y).\]](//latex.artofproblemsolving.com/7/9/e/79e9b17e39cd2c0466afbdc665b6d09a07d9a50e.png)



![\[f(x) = f(f(f(x)) + y) + f(xf(y)) f(x+y).\]](http://latex.artofproblemsolving.com/7/9/e/79e9b17e39cd2c0466afbdc665b6d09a07d9a50e.png)
Plan ahead for the next school year. Schedule your class today!
Something appears to not have loaded correctly.