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Question

The domain of the function f(x)=log|logx|, is
  1. (,1)(1,)
  2. (,1)
  3. (0,1)(1,)
  4. (1,)


Solution

The correct option is C (0,1)(1,)
We have,
f(x)=log|logx|

f(x) is defined when
|logx|>0 and x>0
x1 and x>0
x(0,1)(1,)

Hence, domain of the function f(x) is (0,1)(1,).

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