I know how to determine injectivity and surjectivity for maps between regular sets, but in this case I've got some problems. How can I solve this?
Given the following map $\psi:\overline{x} \in \mathbb{Z}_{16}\mapsto \overline{7}\overline{x}\in\mathbb{Z}_{16}$. Without calculating a single element's image, and just using the properties of $\overline{7}$ in $\mathbb{Z}_{16}$, decide if $\psi$ is injective, surjective or both. If possible, find the inverse of $\psi$.