Question

Find the domain and range of $f\left(x\right)=\{(x,\frac{1}{1-x^2}):x\in Rx\ne \pm 1\}$

Answer 1

Given $f\left(x\right)=\left\{\right(x,\frac{1}{1-x^2}),xϵRx\ne \pm 1\}$

Domain of $f\left(x\right)$ is $(-\infty ,\infty )-\{-1,1\}$

range of $f\left(x\right)$ is $(-\infty ,1)-\left\{0\right\}$