Question

If $f\left(x\right)=x^2+1,$ , then $f^{-1}\left(17\right)$ will be

• A. $4,-4$
• B. $4,0$
• C. $3,2$
• D. None

Answer 1

The correct option is A $4,-4$

$f\left(x\right)=x^2+1,y\left(say\right)$

$\Rightarrow y=x^2+1$

$\Rightarrow x=\pm \sqrt{y-1}$

$\Rightarrow y=\pm \sqrt{x-1}=f^{-1}\left(x\right)$

$\Rightarrow f^{-1}\left(17\right)=\pm \sqrt{17-1}$

$=\pm 4$