Let f : R R be defined by f ( x ) = x 2 + 1 . Then, pre-images of 17 and - 3 , respectively, are:

Question

Let $f : R \to R$ be defined by $f (x) = x^{2} + 1$ . Then, pre-images of 17 and $- 3$ , respectively, are:

Smart Achievers · Accepted Answer

(3)

Ans. ${4, - 4}, ϕ$

Explanation:

Since for $f^{- 1} (17) = x$

$\Rightarrow$ $f (x) = 17 or x^{2} + 1 = 17$

$\Rightarrow$ $x = \pm 4$

or $f^{- 1} (17) = {4, - 4}$

and for $f^{- 1} (- 3) = x$

$\Rightarrow$ $f (x) = - 3$

$\Rightarrow$ $x^{2} + 1 = - 3$

$\Rightarrow$ $x^{2} = - 4$

Hence, $f^{- 1} (- 3) = ϕ$

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