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Let f:R to R be a function given by f(...

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)=1+xg(x),log_(e)2, "where "underset(x to 0)lim g(x)=1. "Then, f'(x)=`

A

`f'(x)` does not exist

B

`f'(x)=2f(x)` for all x

C

`f'(x)=f(x)` for all x

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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