Big-O: If $f(n)=O(g(n))$, prove $2^{f(n)}=O(2^{(g(n)})$

Suppose that both f(n) and g(n) are non-negative functions. If $f(n)=O(g(n))$, is $2^{f(n)}=O(2^{(g(n)})$ true too? If not, give counter examples.

I am unsure of how to proceed. What I have in mind at the moment is that since f(n) and g(n) are non-negative functions, making them functions exponents to 2 (as the base) would not change their characteristics. I would appreciate help in understanding this problem and proving it.

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