Chapter 4.1, Problem 47E

A function $f\left(t\right)$ from $ℝ$ to $ℝ$ is called even if $f\left(-1\right)=f\left(t\right)$ , for all t in $ℝ$ , and odd if $f\left(-1\right)=-f\left(t\right)$ , for all t. Are the even functions a subspace of $\text{F}\left(ℝ,ℝ\right)$ , the space of all functions from $ℝ$ to $ℝ$ ? What about the odd functions? Justify your answers carefully.