If x is a real number, then \sqrt{\log_e {4x-x^2}/3} is a real number if and only if

Correct Answer is : 1 ≤ x ≤ 3

CAT 2019 Shift 2 Paper

Question : 83 of 100

Marks: +1, -0

If x is a real number, then

√{\log_e {4x-x^2}/3}

is a real number if and only if

Solution:

The expression will be real only if

\log _{e} \;{4 x-x^{2}}/{3} ≥ 0

\;{4 x-x^{2}}/{3} ≥ e^{0}

⇒ \;{4 x-x^{2}}/{3} ≥ 1

⇒ 4 x-x^{2} ≥ 3

⇒ x^{2}-4 x+3 ≤ 0

⇒(x-1)(x-3) ≤ 0

1 ≤ x ≤ 3

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