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How to Find the Inverse of a Function

f: R→ R is de...

Question

$f : R \to R$ is defined by $f (x) = x^{2} - 5 x$ . Then the inverse image set of ${- 6}$ is?

ϕ

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{3, 2}

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{3}

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{- 3, - 2}

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Solution

The correct option is D ${3, 2}$
For inverse image set of ${- 6}$
we have, $x^{2} - 5 x = - 6$
$x^{2} - 5 x + 6 = 0$
$x^{2} - 3 x - 2 x + 6 = 0$
$(x - 2) (x - 3) = 0$
Hence, the set is ${3, 2}$

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