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Class 11 Mathematics Relations and Functions Real-Valued Functions, Their Domain and RangeExpert

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What is the domain of (f(x)=\sqrt{\log_{\frac{1}{2}}(x-4)})?

Answer and explanation

Correct answer: ( (4,5] )

The square root needs (\log_{\frac{1}{2}}(x-4)\ge 0) and (x-4>0). Since the base (\frac{1}{2}<1), (0<x-4\le 1), so the domain is ((4,5]).

Related tags

Real-Valued-Functions Domain Logarithm Radical Real Valued Functions Their Domain And Range Real Valued Functions Their Domain And Range Relations And Functions Mathematics

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