The domain of the function f(x) = sqrt{log_{1 | vedclass

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Question

(B) For the function $f(x) = \sqrt{\log_{10}\left(\frac{5x - x^2}{4}\right)}$ to be defined, the expression inside the square root must be non-negativ

Vedclass · Accepted Answer

$[1, 4]$

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(B) For the function $f(x) = \sqrt{\log_{10}\left(\frac{5x - x^2}{4}\right)}$ to be defined, the expression inside the square root must be non-negative: $\log_{10}\left(\frac{5x - x^2}{4}\right) \geq 0$. This implies $\frac{5x - x^2}{4} \geq 10^0$, which simplifies to $\frac{5x - x^2}{4} \geq 1$. Multiplying by $4$, we get $5x - x^2 \geq 4$, or $x^2 - 5x + 4 \leq 0$. Factoring the quadratic, we have $(x - 1)(x - 4) \leq 0$. This inequality holds when $x \in [1, 4]$. Thus, the domain of $f(x)$ is $[1, 4]$.

The domain of the function $f(x) = \sqrt{\log_{10}\left(\frac{5x - x^2}{4}\right)}$ is:

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