Question

请帮忙解决一道证明子空间的线性代数问题，谢谢！

We say a function f:R→R has integer period if there exists a positive integer a such that f(x)=f(x+a). Is the set W={f∣f has integer period} a subspace of F(R)? Explain your answer.

Answer 1

if f1 belongs to W, kf1 belongs to W too
if f1, f2 belong to W, f1 +f2 belong to W too
so W is a subspace of F(R)