Question

Let $f:Z\to Z$ be defined by $f\left(x\right)=x^2$ then find $f^{-1}\left(25\right)$. Where $Z$ is the set of integers.

Answer 1

Given, $f:Z\to Z$ be defined by $f\left(x\right)=x^2$.

Let $f^{-1}\left(25\right)=y$

or, $f\left(y\right)=25$

or, $y^2=25$

or, $y=\pm 5$.

So $f^{-1}\left(25\right)=\{-5,5\}$.