IMO

Algebra Level 4

How many functions f : R → R f: \mathbb{R}\rightarrow \mathbb{R} satisfy the equation f ( x + f ( x + y ) ) + f ( x y ) = x + f ( x + y ) + y f ( x ) f(x+f(x+y))+f(xy)=x+f(x+y)+yf(x) for all real numbers x x and y ? y?

3 2 4 1

Nguyen Thanh Long by Nguyen Thanh Long , 39, Vietnam

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1 solution

True answer is 2.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

f(x)=x and f(x)=2-x.

Anatoliy Kazmerchuk - 5 years, 10 months ago

Do you have proof?

Alan Yan - 4 years, 6 months ago

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