f-x-f-y-2-f-x-y-2-x-y-R-f-x-

Question Number 1668 by 123456 last updated on 30/Aug/15

\frac{f (x) + f (y)}{2} = f (\frac{x + y}{2}), \forall x, y \in R

f (x) = ?

Commented by Rasheed Ahmad last updated on 30/Aug/15

f (x) h a s t w o p r o p e r t i e s :

(1) f (c x) = c f (x) f o r c o n s t a n t c

(2) f (x + y) = f (x) + f (y)

Answered by prakash jain last updated on 02/Sep/15

f (x) = k x