Suppose $\phi:\mathbb{Z}\_{50} \rightarrow \mathbb{Z}\_{15}$ is a group homomorphism with $\phi(7)=3$. 

(a) Determine $\phi(x)$

(b) Determine the image of $\phi$

(c) Determine the kernel of $\phi$. 

(d) Determine $\phi^{-1}(3)$. 
[![enter image description here](https://i.stack.imgur.com/JAsOY.png)](https://i.stack.imgur.com/JAsOY.png)

**Why is the Kernel such that $5|x$?**