Let $\mathrm{f}: \mathrm{X} \rightarrow \mathrm{Y}, \mathrm{A} \subset \mathrm{X}$ and $\mathrm{B} \

Question

Let $\mathrm{f}: \mathrm{X} \rightarrow \mathrm{Y}, \mathrm{A} \subset \mathrm{X}$ and $\mathrm{B} \subset \mathrm{Y}$. If $f(A)=\{y: y=f(x)$ for some $x \in A\}$ and $\mathrm{f}^{-1}(\mathrm{~B})=\{\mathrm{x}: \mathrm{f}(\mathrm{x}) \in \mathrm{B}\}$, then

Professor PC Thomas Classes · Answer

If $f$ is one - one then $f^{-1}(f(A))=A$ and if f is onto then $\mathrm{f}\left(\mathrm{f}^{-1}(\mathrm{~B})\right)=\mathrm{B}$