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  4. The domain of definition of the function f(x)=√ log 10( (5x-x2/4) ) is:

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

JamiaJamia 2005

Solution:

The function $ f(x)=\sqrt{{{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right)} $ exists for $ \frac{5x-{{x}^{2}}}{4}\ge 1 $ $ \Rightarrow $ $ 5x-{{x}^{2}}-4\ge 0 $ $ \Rightarrow $ $ x\in [1,4] $