Let T be the ring of all continuous functions from R to R and let S={f belonging to T such that f(2)=0} Is S a subring of T? Give a proof.

I believe it is.

Closed under addition by letting f belong to T so that f(2)=0 and g belong to T so that g(2)=0. By prop. of cont. functions (f+g)(2)=0 and (fg)(2)=0.

I don't know what the 0 element is in this context. Is it just h(x)=f(2)=0?

I also am not sure about showing that the solution to a+x=0t is in S....

Thanks.