Aspire Faculty ID #15394 · Topic: MAH MCA CET 2023 · Just now
MAH MCA CET 2023

$f(x) = \sqrt{\log_{1/4}\left(\dfrac{5x - x^2}{4}\right)}$, find the domain of $f(x)$.

Solution

For $\log_{1/4}\left(\dfrac{5x - x^2}{4}\right)$ to be $\ge 0$, $\dfrac{5x - x^2}{4} \le 1$ since base $< 1$. Simplifying gives $x = 1, 4$. Hence, domain $= {1,4}$.

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