Find the domain of :- f(x) = log1/2(-log2(1+1/(x)1/4)-1) in detail

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Please find below the solution to the asked query:

fx=log12-log21+1x14-1Now log2X is negative when X<1 and positive when X>1Here 1+1x14>0 for all values of x Except 0 for which it is undefinedHence log21+1x14 >0 for all defined values of x. -log21+1x14<0 -log21+1x14<0 -log21+1x14-1<0Hence quantity inside log12  is negative. But for log to be defined it argument should be strictly positive.Hence =log12-log21+1x14-1 will not be defined for all real vaues ofx.Hence domain of fx is x 

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