If a function g(x) which has derivaties ...

If a function g(x) which has derivaties g'(x) for every real x and which satisfies the following equation `g(x+y) = e^(y)g(x) + e^(x)g(x)` for all x and y and g'(0) = 2, then the value of `{g'(x) - g(x)}` is equal to

A

`e^(x)`

B

`(2)/(3) e^(x)`

C

`(1)/(2) e^(x)`

D

`2 e^(x)`

Verified by Experts

The correct Answer is:

D

Similar Questions

Explore conceptually related problems

f'(x) = g(x) and g'(x) =-f(x) for all real x and f(5)=2=f'(5) then f^2 (10) + g^2 (10) is

If f(x)=ax+b and g(x)=cx+d, then f(g(x))=g(f(x)) is equivalent to

f(x)= 3x^(2)-1 and g(x)= 3 + x . If f= g then the value of x is…….

If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x) , then the value of g'(1) is

If f(x) - g(x) is constant then f'(x) = g'(x)

Find the values of x for which the functions f(x)= 3x^(2)-1 and g(x)= 3 + x are equal

If the functions f(x)=x^(5)+e^(x//3) " and " g(x)=f^(-1)(x) , the value of g'(1) is ………… .

If f and g are real functions defined by f(x)= x^(2) + 7 and g(x)= 3x + 5 . Then, find each of the following f(3) + g(-5)

f(x)= x, g(x)= (1)/(x) and h(x)= f(x) g(x). If h(x) = 1 then…….

If f(x)= sqrtx and g(x)= x be two functions defined in the domain R^(+) uu {0} , then find the value of (f+g) (x) .