2. Suppose f(x) is a function such that f(x) = O(1) (big o)

a) Can e^{f(x)} =o(1)?

I know if f(x)=o(g(x)), then f(x)=O(g(x))

how about the otherwise? is that no. its not possible bigger than 1 while smaller than 1.?

b) Find one such function f(x) which is not o(1) but where f(2009)=0

no idea.