Question 12.

If x is a real number, then $\sqrt{\log_{e}{\frac{4x - x^2}{3}}}$ is a real number if and only if

A

1 \leq x \leq 3

B

1 \leq x \leq 2

C

-1 \leq x \leq 3

D

-3 \leq x \leq 3

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Text Explanation

$\sqrt{\log_{e}{\frac{4x - x^2}{3}}}$ will be real if $\log_e \frac{4x-x^2}{3} \ge 0$

$\frac{4x-x^2}{3} \ge 1$

$4x-x^2-3 \ge 0$

$x^2-4x+3 \le 0$

1=< x=< 3

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