Question 1026858
We can use the subspace criterion: The subset W is a subspace of V if for any f(x), g(x) in W then every linear combination {{{c[1]f(x)+c[2]g(X)}}} would also be in W.

This is almost automatic, clearly {{{c[1]f(0)+c[2]g(0) = c[1]f(1)+c[2]g(1)}}} since f(0) = f(1) and g(0) = g(1).

Thus, W is a subspace of V.