Re: Equality of functions

it's always included in C, that's all we can say. Exemple f R-R x|-> x², and C is [-4,4], we have f(f^-1(C))=[0,4] =/= C

Re: Equality of functions

Could I just write $\displaystyle f(f^{-1}(C))=\{y| y \in C \wedge \exists_{x \in X}(f(x)=y)\}$? Because $\displaystyle f(f^{-1}(C)) $ equals the elements of C that can be reached from X.

Re: Equality of functions

Quote:

Originally Posted by

**MachinePL1993** For some function $\displaystyle f:X \rightarrow Y$ and $\displaystyle C \subseteq Y$ I have to find something, that would equal $\displaystyle f(f^{-1}(C)) = ?$.

This is much like your other post.

$\displaystyle f(f^{-1}(C)) = C$ if and only if $\displaystyle f$ is surjective.

Re: Equality of functions