The domain of the real valued function f(x) = | vedclass

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(A) Given the function $f(x) = \frac{\sqrt{\log _{0.5}(x-3)}}{\sqrt{x-1}}$.For the square root in the numerator to be defined,we must have $\log _{0.5

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$(3, 4]$

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(A) Given the function $f(x) = \frac{\sqrt{\log _{0.5}(x-3)}}{\sqrt{x-1}}$.For the square root in the numerator to be defined,we must have $\log _{0.5}(x-3) \geq 0$.Since the base $0.5 Also,for the logarithm to be defined,$x-3 > 0$,which implies $x > 3$.For the denominator to be defined and non-zero,$x-1 > 0$,which implies $x > 1$.Taking the intersection of all conditions: $(x \leq 4) \cap (x > 3) \cap (x > 1)$,we get $3 Thus,the domain is $(3, 4]$.

The domain of the real valued function $f(x) = \frac{\sqrt{\log _{0.5}(x-3)}}{\sqrt{x-1}}$ is

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