Home
Class 12
MATHS
Let f:R to R be a function given by 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)=1+xg(x)+x^(2) g(x) phi(x)"such that "underset(x to 0)lim g(x)=a and underset(x to 0)lim phi(x)=b,` then f'(x) is equal to

A

`(a+b)f(x)`

B

`af(x)`

C

`bf(x)`

D

`-f(x)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

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)+x^(2) g(x) phi(x)"such that "lim_(x to 0) g(x)=a and lim_(x to 0) phi(x)=b, then f'(x) is equal to

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 given by f(x+y) = f(x) + f(y) for all x,y in R such that f(1)= a 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)=1+xg(x),log_(e)2, "where "lim_(x to 0) g(x)=1. "Then, f'(x)=

Let f:R in R be a function given by f(x+y)=f(x) f(y)"for all"x,y in R "If "(x) ne 0,"for all "x in R and f'(0)=log 2,"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 to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,

Let f:R to R be a function satisfying f(x+y)=f(x)+f(y)"for all "x,y in R "If "f(x)=x^(3)g(x)"for all "x,yin R , where g(x) is continuous, then f'(x) is equal to

Let f be a function satisfying f(x+y)=f(x) *f(y) for all x,y, in R. If f (1) =3 then sum_(r=1)^(n) f (r) is equal to