If $$f(x)=log$$[x−$$1$$]⁡|x|x, where [.] denotes the greatest integer function, then

Correct option is 2D(f)=[3,∞),R(f)={0}

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If $f (x) = \log_{[x - 1]} \frac{| x |}{x}$ , where [.] denotes the greatest integer function, then

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D(f)=[3,∞),R(f)={0,1}

D(f)=[3,∞),R(f)={0}

D(f)=(2,∞),R(f)={0,1}

D(f)=(3,∞),R(f)={0}

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detailed solution

Correct option is B

f(x) is defined for all x satisfying[x−1]>0,[x−1]≠1 and |x|x>0.Now, [x−1]>0,[x−1]≠1⇒x∈[3,∞)and , |x|x>0⇒x>0∴ D(f)=[3,∞)Clearly, |x|x=1 for all x∈[3,∞)∴ f(x)=log[x−1]⁡|x|x=log[x−1]⁡1=0So, R(f)={0}

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If f(x)=log[x−1]⁡|x|x, where [.] denotes the greatest integer function, then

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If $f (x) = \log_{[x - 1]} \frac{| x |}{x}$ , where [.] denotes the greatest integer function, then