Functional Functions that Function

Find all functions f:R→Rf : \mathbb{R} \rightarrow \mathbb{R} such that f(x+y)+2f(x−y)+f(x)+2f(y)=4x+yf (x + y) + 2f (x - y) + f (x) + 2f (y) = 4x + y for all real xx and yy.

#Algebra

Note by Yuxuan Seah
6 years, 10 months ago

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Comments

For all x, f(x)=0 I HAVE A PROOF BUT AM HAVING PROBLEM TO POST IT. Hence, I GIVE THE STRATERGY PLUG y=0, You get f(x)=x-r where 2r=f(0) Then plugging in for functions we get 8r=0 GIVING THE RESULT r=0 AND HENCE, f(x)=x for all x

A Former Brilliant Member - 6 years, 10 months ago

SORRY, I MISTYPED IN THE FIRST LINE,f(x)=0 but it is f(x)=x

A Former Brilliant Member - 6 years, 10 months ago
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