Let $f: \mathbb{Z}_5 \rightarrow \mathbb{Z}_{10}$ and $g: \mathbb{Z}_5 \rightarrow \mathbb{Z}_{10}$ be defined by $f([x]_5)=[x]_{10}$ and $g([x]_5)=([x]_{10})^5$ Prove that $f=g$
I know that the domain and codomain are the same but I'm unsure how to go about showing that for every input both functions have the same output.