"F is the vector space of functions defined in R with real variables. Is the subset of funtions of which f(1)=0 a subspace of F?"

Question

I don't even really understand the question to begin with and not exactly what I have to I desperately need help haha!

"F is the vector space of functions defined in R with real variables. Is the subset of funtions of which f(1)=0 a subspace of F?"

Answer 1

The subset of such functions is closed under addition (if $f(1)=g(1)=0$ then $[f+g](1)=f(1)+g(1)=0$) and multiplication by a scalar (if $f(1)=0$ then $[\lambda f](1)=\lambda f(1)=0$ for any $\lambda \in \mathbb{R}$).

Hence it is a subspace by definition.