SOLUTION: If f(x+y) = f(x) + f(y) x€R and y€R then f(0) equals to what

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Question 1040827: If f(x+y) = f(x) + f(y) x€R and y€R then f(0) equals to what
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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Then 

  f(x) = f(x+0)              ( <--- since x = x+0 )
= f(x) + f(0)                ( <--- since f(x+y) = f(x) + f(y) )

Thus we get 

  f(x) = f(x) + f(0).

Now distract f(x) from both sides. You will get

  0 = f(0),  or  f(0) = 0.

Answer.  Then f(0) = 0.