Home
Class 12
MATHS
Let f : R to R be a function such that ...

Let ` f : R to R` be a function such that
`f(x+y) = f(x)+f(y),Aax, y in R.` If f (x) is differentiable at x = 0, then

A

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

B

f(x) is continuous `AA x epsilonR`

C

`f'(x)` is constant `AA x epsilonR`

D

`f(x)` is differentiable except at finitely many points

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f:R to R be a function such that f(x+y)=f(x)+f(y)"for all", x,y in R If f(x) is differentiable at x=0. then, which one of the following is incorrect?

Let f:R rarr R be a function such that f(x+y)=f(x)+f(y),AA x,y in R

Let f(x+y)=f(x)+f(y)AA x, y in R If f(x) is continous at x = 0, then f(x) is continuous at

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

Let f : R to R be a function given by f(x+y)=f(x)f(y) for all x , y in R If f(x) ne 0 for all x in R and f'(0) exists, then f'(x) equals

Let f:R rarr R be a function such that f((x+y)/(3))=(f(x)+f(y))/(3),f(0)=0 and f'(0)=3

Let f:R rarr R be a function given by f(x+y)=f(x)f(y) for all x,y in R .If f'(0)=2 then f(x) is equal to

Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(xy+1)=f(x)f(y)-f(y)-x+2. Then f is