Birthday Problem!

Algebra Level 5

f ( x + y ) ⩽ y f ( x ) + f ( f ( x ) ) \large \displaystyle f(x+y) \leqslant yf(x)+f(f(x))

Let f : R → R f:\mathbb{R} \rightarrow \mathbb{R} be a real-valued function defined as shown above for all real numbers x x and y y . Find f ( − 5699 ) \displaystyle f(-5699) .


The answer is 0.

Saarthak Marathe by Saarthak Marathe , 22, India

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1 solution

on observation , we are not needed to find the function if f(x)=0 it satisfies 0<=0 , so it mus be true , why is this problem given such a high rating of level 5 ? relevant WIKI : here

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