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

(0, 2]

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(- \infty, 2]

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(0, 9]

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N o n e o f t h e s e

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Solution

The correct option is A $(0, 2]$
$y = {log}_{3} (5 + 4 x + x^{2})$
For $y - x^{2} + 4 x + 5$ we have
$\frac{- b}{2 a} = \frac{- 4}{- 2} = 2 = x$
Put $x = 2$
$- 4 + 8 + 5 = 9$
Mac value $= 9$
$∴ y = {log}_{3} (9) = 2$
Also min value $\sim 1$
Range $= (0, 2)$

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