$h (x) = \frac{1}{{(x - 5)}^{2} + 4 (x - 5) + 4}$
For what value of $x$ is the function $h$ above undefined?

3

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2

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6

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4

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Solution

The correct option is A $3$
The function is undefined when its denominator $= 0$
Thus, $(x - 5)^{2} + 4 (x - 5) + 4 = 0$
$=> x^{2} - 10 x + 25 + 4 x - 20 + 4 = 0$
$=> x^{2} - 6 x + 9 = 0$
$=> (x - 3)^{2} = 0$
$=> x = 3$

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