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 \(\frac{4x-x^2}{3}  ≥ e^0.\)

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