Discussion

Question:

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

Explanation:

It is given that, $\sqrt{\log_{e} (\frac{4 x - x^{2}}{3})}$ is a real number

Therefore, $\log_{e} (\frac{4 x - x^{2}}{3})$ ≥ 0

⇒ $\frac{4 x - x^{2}}{3}$ ≥ 1

⇒ 4x – x² ≥ 3

⇒ x² - 4x + 3 ≤ 0

⇒ (x - 1)(x - 3) ≤ 0

⇒ x ∈ [1, 3]

Hence, option (c).

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