Inverse Image Intersection Equality and Counterexample of a Function Proof

Suppose f is a function with sets A and B.

1. Show that:

2. Show by giving a counter example that:

1.

Let c be an element of .

By the definition of , there is a so that .

Since, , . Since . This follows alongside .

Since and .

Thoughts? Also would I need to show that the to show true equality?

2.

I'm thinking either the absolute value function or a square function of some sort would show that it is not equal. Though, I'm not sure how to proceed with depicting the counter example.