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Domain

Find the doma...

Question

Find the domain of definition of the following function:
$f (x) = log (5 x^{2} - 8 x - 4) + \sqrt{x - 1}$

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Solution

$5 x^{2} - 8 x - 4 > 0 5 x^{2} - 10 x + 2 x - 4 > 0 5 x (x - 2) + 2 (x - 2) > 0 (x - 2) (5 x + 2) > 0 x \in (- \infty, \frac{- 2}{5}) \cup (2, \infty)$

$x - 1 \geq 0 x \geq 1$
Taking intersection we get
$x \in (2, \infty)$

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