The domain of function $y = {log}_{3} (5 + 4 x - x^{2})$ is

(0, 2]

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(- \infty, - 1) \cup (5, \infty)

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(0, 9]

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(- 1, 5)

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Solution

The correct option is D $(- 1, 5)$
$y = {log}_{3} (5 + 4 x - x^{2})$

$∴ 5 + 4 x - x^{2} > 0$

$x^{2} - 4 x - 5 < 0$

$(x - 5) (x + 1) < 0$

$x < 5$ and $x > - 1$

$x \in (- 1, 5)$

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