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Arithmetic Progression

Find the doma...

Question

Find the domain of definition of the following function:
$y = log (1 - log (x^{2} - 5 x + 16)) .$

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Solution

$1 - log (x^{2} - 5 x + 16) > 0 1 > log (x^{2} - 5 x + 16) 10 > x^{2} - 5 x + 16 x^{2} - 5 x + 6 < 0 (x - 3) (x - 2) < 0 x \in (2, 3)$
Also,
$x^{2} - 5 x + 16 > 0 x \in R$
Taking intersection,
$x \in (2, 3)$

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