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Find the domain of the function f(x)=log₂ (-log_(1/2)(1+1/x^(1/4))-1).

1. (0, 1)
2. (0, 1]
3. [1, ∞)
4. (1, ∞)

Correct answer: (0, 1)

Solution

The function involves a logarithm, which requires its argument to be positive. The inner logarithm, -log_(1/2)(1+1/x^(1/4))-1, must also be positive, leading to constraints on the values of x. Analyzing these conditions reveals that the valid domain is (0, 1), where the expression remains defined.

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