determine whether w={f:f(x)greater than or equal to 0} is a subspace of C, the set is continuous functions on the real numbers
No, it isn't. Look at DrSteve's post. For example choose $\displaystyle f(x)=1$ for all $\displaystyle x\in \mathbb{R}$ then, $\displaystyle f\in W$ however $\displaystyle [(-1)f](x)=(-1)f(x)=(-1)\cdot 1=-1$ . That is, $\displaystyle (-1)f\not\in W$ .
Fernando Revilla
Sorry, by error I thought your post was from the original poster.
Fernando Revilla