Question

If $f:R\to R$ is defined by $f\left(x\right)=x^2+1$, then 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

Answer: (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 value of $x$.
Hence, $f\left(17\right)=\{-4,4\}\text{and}{f}^{-1}(-3)=\varphi .$