SOLUTION: Please help me find the domain of the function: f(x)=(cosx-sinx)^(1/2). Df={xcR; cosx-sinx>=0}.

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Question 1014385: Please help me find the domain of the function: f(x)=(cosx-sinx)^(1/2).
Df={xcR; cosx-sinx>=0}.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You know that cos%28x%29=sin%28x%29 at x=%281%2F4%29pi, x=%283%2F4%29pi,x=%285%2F4%29pi, and x=%287%2F4%29pi so check intermediate values to see if cos%28x%29-sin%28x%29%3E=0.
So I would check at x=0, x=pi%2F2, x=pi, and x=%283%2F2%29pi
cos%280%29-sin%280%29%3E0
1-0%3E0
1%3E0
True.
cos%28pi%2F2%29-sin%28pi%2F2%29%3E0
0-1%3E0
-1%3E0
False.
cos%28pi%29-sin%28pi%29%3E0
-1-0%3E0
-1%3E0
False.

cos%28%283%2F2%29pi%29-sin%28%283%2F2%29pi%29%3E0
0-%28-1%29%3E0
1%3E0
True.
So the domain would be from x=0 to x=pi%2F4 and from x=%285%2F4%29pi to x=2pi inclusively and 2pi multiples.