If a function f:RrarrR, where R is the s...

If a function f:R`rarr`R, where R is the set of real numbers satisfying the equation
f(x+y)=f(x)+f(y), `AA` x,y. If f(x) is continuous at x=0, then

A

f(x) is discontinuous, for all `x in R`

B

f(x) is continuous, for all `x in R`

C

f(x) is continuous for `xin{1,2,3,4}`

D

None of the above

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The correct Answer is:

B

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