- #1

SMA_01

- 218

- 0

## Homework Statement

Let f:S→T and let A[itex]\subseteq[/itex]T. Define the preimage of A as f

^{-1}(A)={x in S: f(x) is in A}.

Demonstrate that for any such map f and B[itex]\subseteq[/itex]ran(f), f(f

^{-1}(B)) = B.

I am going to use set inclusion to prove this, but can I use function composition in the portion in red? I was going to say an element y is in f(f

^{-1}(B)) and then was thinking to apply function composition so as to map an element x back to S then apply f to it and map the new element to B.

Does this seem right?

Thanks.