Functional Equations

Can anyone help me with this functional equation:

\(f(f\left( x+y \right) )\quad =\quad x\quad +\quad f(y)\quad \)

I'm quite new to the topic so if anyone has any resources, I would be very grateful!

Thanks

Note by Soham Karwa
4 years ago

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put x=0 to get f(f(y)) = f(y) therefore f(f(x+y)) = f(x+y) = x + f(y) put y=0 to get f(x) = x + a for some constant a. putting this back in the problem, 2a=a and so f(x) = x for all real x..

Hemang Sarkar - 3 years, 11 months ago

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