The domain of the function log( log sin(x) ) is
2018
The domain of the function log( log sin(x) ) is
- A.
0 < x < π
- B.
2nπ < x < (2n + 1) π , for n in N
- C.
Empty set
- D.
None of the above
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Correct answer: C
To find the domain of f(x) = log(log(sin x)), we analyze the conditions for both logarithms.
1. The inner logarithm log(sin x) requires sin x > 0.
2. The outer logarithm log(log(sin x)) requires the argument to be positive: log(sin x) > 0.
3. Solving log(sin x) > 0 gives sin x > e^0, which simplifies to sin x > 1.
4. Since the range of sin x is [-1, 1], it can never be greater than 1.
Therefore, no real values of x satisfy these conditions. The domain is the empty set.