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The values of...

Question

The values of $x$ for which the function $f (x) = \frac{x^{2} + x + 1}{x^{2} - 7 x + 12}$ is not defined, is

A

{3, 4}

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B

{3, - 4}

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C

{- 3, - 4}

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D

the function is defined everywhere

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Solution

The correct option is A ${3, 4}$
$f (x) = \frac{x^{2} + x + 1}{x^{2} - 7 x + 12}$
It is a rational function, so the function is not defined when the denominator is equal to zero.
$x^{2} - 7 x + 12 = 0 \Rightarrow (x - 3) (x - 4) = 0 \Rightarrow x = 3, 4$

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