Question 1040827
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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.

<U>Answer</U>.  Then f(0) = 0.
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