The domain of the function sqrt{log left( fra | vedclass

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Question

(B) For the function $f(x) = \sqrt{\log \left( \frac{5x - x^2}{6} \right)}$ to be defined,the expression inside the square root must be non-negative:$

Vedclass · Accepted Answer

$[2, 3]$

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(B) For the function $f(x) = \sqrt{\log \left( \frac{5x - x^2}{6} \right)}$ to be defined,the expression inside the square root must be non-negative:$\log \left( \frac{5x - x^2}{6} \right) \ge 0$Since the base of the logarithm is $10$ (implied),this inequality is equivalent to:$\frac{5x - x^2}{6} \ge 10^0$$\frac{5x - x^2}{6} \ge 1$$5x - x^2 \ge 6$$x^2 - 5x + 6 \le 0$Factoring the quadratic expression,we get:$(x - 2)(x - 3) \le 0$The inequality holds when $x$ lies between the roots of the quadratic equation,inclusive:$2 \le x \le 3$Thus,the domain is $[2, 3]$.

The domain of the function $\sqrt{\log \left( \frac{5x - x^2}{6} \right)}$ is

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