Question

Find the range of $f\left(x\right)={\tan }^{-1}\left(\sqrt{x^2-2x+2}\right).$

Answer 1

$f\left(x\right)=ta{n}^{-1}\left(\sqrt{x^2-2x+3}\right)=ta{n}^{-1}[2,\infty ]\equiv \left[ta{n}^{-1}\right(2),\frac{\pi }{2}]$