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Definition of Functions

Let f:R → R...

Question

Let $f : R \to R$ be a function given by $f (x) = x^{2} + 1$ . Find $f^{- 1} (- 5)$ .

A

ϕ

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B

15

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C

0

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D

12

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Solution

The correct option is A $ϕ$
Let $f^{- 1} (- 5) = x$ . Then,
$f (x) = - 5$
$x^{2} + 1 = - 5$
$x^{2} = - 6$
This equation is not solvable for R. Therefore, there is no pre-image of -5. So, $f^{- 1} (- 5) = ϕ$ .

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