MathB.in
New
Demo
Tutorial
About
Did not begin the proof correctly. Create a two-subset proof. In order to show that $f^{-1}(f(C)) \subseteq C$, let $x \in f^{-1}(f(C))$. By definition, it follows that $f(x) \in f(C)$. If you let $y = f(x)$, then you can conclude from the definition of $f(C)$ that there exists a $c \in C$ so that $y = f(c)$. Recalling that $f(x) = y$ you obtain $f(x) = f(c)$. Then use the assumption that $f$ is injective to conclude that $x=c$ and finish the proof. To prove that $ f^{-1}(f(C)) \subseteq C$ use a previously proved Theorem.
ERROR: JavaScript must be enabled to render input!
Thu, 16 Sep 2021 00:15 GMT