Question

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

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

Answer 1

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

Let $y=x^2+1$.

then for $y=17,$ we have $x=\pm 4$ and for $y=-3,x$ becomes imaginary that is, there is no real value of $x$.
Hence, $f^{-1}\left(17\right)=\{4,-4\}$ and $f^{-1}(-3)=\varphi$

Hence, (D) is correct option.