Let a function f: R to R, where R is the...

Let a function `f: R to R`, where R is the set of real nos. satisfying
the equation `f(x+y) = f(x) + f(y) AA x, y` if f(x) is continuous at x = 0,
then

A

(a) f(x) is discontinuous `AA k in R -{1}`

B

(b) f(x) is continuous `AA k in R `

C

(c) f(x) is continuous `AA k in R -{1,2}`

D

(d) none of these

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The correct Answer is:

B

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