If you are able to use such impressive vernacular, as stated in this qoute, then I am supremely confident that you can find all x for which the function is defined.
But, here's my 2 cents anyway
We must find all values of x such that the quotient inside the radical is greater than zero, while the denominator is not equal to zero.
A quotient is positve only if the numerator and denomiator are both positive, or both negative.
is always greator to or equal to zero. This fact makes are task much easier. Now, all we have to do is find when
We Know that the only place at which 1-cos(x) is zero in the interval is at , and greator than zero every where else.
eg
So the domain of the function is
I'm not sure I understand. x is an element of E, not R.
Perhaps this is over my head... But it seems to me as if you've given a general solution for the function as if it were initially given for all x.
If we reread the problem without all the snazzy language, all it says is find the domain of the function over the interval