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# Functional Functions that Function

Find all functions $$f : \mathbb{R} \rightarrow \mathbb{R}$$ such that $$f (x + y) + 2f (x - y) + f (x) + 2f (y) = 4x + y$$ for all real $$x$$ and $$y$$.

Note by Yuxuan Seah
3 years, 5 months ago

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

- 3 years, 5 months ago

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

- 3 years, 5 months ago