Domain of the function sqrt{log left{ frac{5x | vedclass

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Question

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

Vedclass · Accepted Answer

$[2, 3]$

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(B) For the function $\sqrt{\log \left\{ \frac{5x - x^2}{6} \right\}}$ to be defined,the expression inside the square root must be non-negative: $\log \left\{ \frac{5x - x^2}{6} \right\} \ge 0$. This implies $\frac{5x - x^2}{6} \ge 10^0$,which simplifies to $\frac{5x - x^2}{6} \ge 1$. Multiplying by $6$,we get $5x - x^2 \ge 6$,which rearranges to $x^2 - 5x + 6 \le 0$. Factoring the quadratic,we get $(x - 2)(x - 3) \le 0$. This inequality holds for $x \in [2, 3]$. Thus,the domain is $[2, 3]$.

Domain of the function $\sqrt{\log \left\{ \frac{5x - x^2}{6} \right\}}$ is

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