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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)`

Text Solution

Verified by Experts

The correct Answer is:
D
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