f(x)= square root of log2(x2 +1).find the domain and range of functions.

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Please find below the solution to the asked query:

fx=log2x2+1For fx to be defined, argument of log should be strictly positive.x2+1>0which is true for xR, x2 is never negative.Hence domain of fx is -, or xR.Now minimum value of x2+1 is 1 when x=0 and log21=0 and as valueof x2 increases  log2x2+1 will also increase.Hence range of fx is [0,)

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