Show that the set of odd functions that are differentiable in the interval [-10, 10] is a vectorial space

Question

Show that $$ V = \left\{ \left. f \in C^1_{[-10,10]} \right| f \text{ is odd} \right\} $$ is a vector space.

i only need to show thee axiom of the lock for addition and multiplication

Answer 1

You mean closure not lock likely.

Let $f,g \in V$ and $a \in \mathbb{R}$. Show that $af \in V$ and $f+g \in V$.