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+2 votes

The domain of the function log (log sin(x)) is:

  1. $0<x<$$\pi$
  2. $2n$$\pi$$<$$x$$<$$(2n+1)$$\pi$, for $n$ in $N$
  3. Empty set
  4. None of the above
in Set Theory & Algebra by Veteran (431k points)
recategorized | 2k views

3 Answers

+8 votes
Best answer
log( log sin(x) )

-1 <= sinx<= +1

log a is defined for positive values of a,

log sin(x)  is defined for sin(x)= (0,1]

Possible values for  log sin(x) = ($-\infty$ , 0]

Domain of log( log sin(x) )=Not defined

Therefore, Answer (c) Empty Set
by Boss (10.8k points)
edited by
there is a difference between range and domain of a function, Question is asking domain not range.
* log sin(x)  is defined for sin(x)= (0,1]
+1 vote
C empty set
by Junior (725 points)
+1 vote
Option C is correct.

We can satisfy inner log using $x=\pi / 2$, but can't satisfy outer log at the same time. Thus, empty set.
by Loyal (5.4k points)

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