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Let f(x) be a continuous and differentia...

Let `f(x)` be a continuous and differentiable function satisfying `f(x + y) = f(x)f(y) AA x,y in R` if `f(x)` an be expressed as `f(x) = 1 + x P(x) + x^2Q(x)` where `lim_(x->0) P(x) = a and lim_(x->0) Q(x) = b,` then `f'(x)` is equal to :

A

`af (x)`

B

`bf (x)`

C

`(a+b) f (x)`

D

`(a+2b) f(x)`

Text Solution

Verified by Experts

The correct Answer is:
A
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