The domain of the function $f(x) = \sqrt{\log_{10} \left(\frac{5x - x^2}{4}\right)}$ is:
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Test boundaries! At $x=1$, we get $\log_{10}(1) = 0$, which is valid under a square root, meaning $1$ must be included (closed interval). At $x=0$, the logarithm argument is $0$, which is undefined, meaning $0$ must be excluded.