MHB Why is the following not true: f(f^(-1)(B))=B?

[OhMyMarkov]

The title says it: why is the following not true: $f(f^{-1}(B))=B$?

Thanks!

 

[Opalg]

Re: Why is the following not true: $f(f^{-1}(B))=B$?

The title says it: why is the following not true: $f(f^{-1}(B))=B$?

Thanks!

You have not given a context for this, but in general if you have a function $f:A\to B$ there is no reason to suppose that the range of $f$ is the whole of $B$. If $f$ is not surjective then $f(f^{-1}(B)) = f(A) \ne B$.