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Let f:R->R be a function such that f(x+y...

Let `f:R->R` be a function such that `f(x+y)=f(x)+f(y),AA x, y in R.`
a. f(x) is differentiable only in a finite interval containing zero
b. f(x) is continuous for all `x in R`
c. f'(x) is constant for all `x in R`
d. f(x) is differentiable except at finitely many points

A

f(x) is differentiable only in a finite interval containing zero

B

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

C

f'(x) is constant for all `x in R`

D

f(x) is differentiable except at finitely many points

Text Solution

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The correct Answer is:
B, C
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