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Given a function ' g' which has a deriva...

Given a function ' g' which has a derivative `g' (x)` for every real x and satisfies `g'(0)=2 and g(x+y)=e^y g(x)+e^y g(y)` for all x and y then: Find g(x).

A

g(x) is increasing for all ` x in [-1,oo)`

B

range of ` g(x)` is `[-2/e ,oo)`

C

`g'' (x) gt 0 AA x`

D

`lim_( x to 0) ( g(x))/(x)=1`

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A, B
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