Question

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≤x≤2
• B. -3≤x≤3
• C. 1≤x≤3
• D. -1≤x≤3

Answer 1

The Correct Option is C

The expression will be real only if $log_e\frac{4x-x^2}{3}  ≥ 0.$
Or $\frac{4x-x^2}{3}  ≥ e^0.$

$⇒$$\frac{4x-x^2}{3}  ≥ 1.$
$⇒ 4x-x^2 ≥ 3$
$⇒ x^2-4x+3≤0$
$⇒(x-1)(x-3)≤0$
$1≤x≤3$