Question

If $f:R\to R$ is defined by $f\left(x\right)=x^2+1$, then values of $f^{-1}$ (17) and $f^{-1}$ (-3) respectively are

• A. $\varphi$, {4, $\sqrt{-}4$}
• B. {3, -3}, $\varphi$
• C. $\varphi$, {3, -3}
• D. {4, -4}, $\varphi$

Answer 1

The correct option is A $\varphi$, {4, $\sqrt{-}4$}

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

$y=x^2+1\iff x=y^2+1$

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

$f^{-1}\left(17\right)=\pm \sqrt{17-1}=4$

$f^{-1}(-3)=\pm \sqrt{-3-1}=\sqrt{-4}$