Let $t \in \mathbb { R }$. Give an expression of $\phi _ { X } ( - t )$ in terms of $\phi _ { X } ( t )$. Deduce a necessary and sufficient condition on the image $\phi _ { X } ( \mathbb { R } )$ for the function $\phi _ { X }$ to be even.
Let $t \in \mathbb { R }$. Give an expression of $\phi _ { X } ( - t )$ in terms of $\phi _ { X } ( t )$. Deduce a necessary and sufficient condition on the image $\phi _ { X } ( \mathbb { R } )$ for the function $\phi _ { X }$ to be even.