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The domain of the function $f (x) = {[\log_{10} (\frac{5 x - x^{2}}{4})]}^{1 / 2}$ is

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-∞

1≤x≤4

4≤x≤16

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detailed solution

Correct option is B

We have fx=log105x-x241/2From ( 1), clearly, f (x) is defined for those values of x for whichlog105x-x24≥0or 5x-x24≥100or 5x-x24≥1or x2-5x+4≤0or x-1x-4≤0Hence, the domain of the function is [1,4].

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The domain of the function fx=log105x-x241/2 is

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The domain of the function $f (x) = {[\log_{10} (\frac{5 x - x^{2}}{4})]}^{1 / 2}$ is