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

#### OhMyMarkov

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

Thanks!

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#### Opalg

##### MHB Oldtimer
Staff member
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 $f(f^{-1}(B)) = f(A) \ne B$.