document.write( "Question 1014385: Please help me find the domain of the function: f(x)=(cosx-sinx)^(1/2).
\n" ); document.write( "Df={xcR; cosx-sinx>=0}. \n" ); document.write( "

Algebra.Com's Answer #631257 by Fombitz(32388) $\"\"$ $\"About$

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 $\"cos%28x%29-sin%28x%29%3E=0\"$ .
\n" ); document.write( "So I would check at $\"x=0\"$ , $\"x=pi%2F2\"$ , $\"x=pi\"$ , and $\"x=%283%2F2%29pi\"$
\n" ); document.write( " $\"cos%280%29-sin%280%29%3E0\"$
\n" ); document.write( " $\"1-0%3E0\"$
\n" ); document.write( " $\"1%3E0\"$
\n" ); document.write( "True.
\n" ); document.write( " $\"cos%28pi%2F2%29-sin%28pi%2F2%29%3E0\"$
\n" ); document.write( " $\"0-1%3E0\"$
\n" ); document.write( " $\"-1%3E0\"$
\n" ); document.write( "False.
\n" ); document.write( " $\"cos%28pi%29-sin%28pi%29%3E0\"$
\n" ); document.write( " $\"-1-0%3E0\"$
\n" ); document.write( " $\"-1%3E0\"$
\n" ); document.write( "False.
\n" ); document.write( "
\n" ); document.write( " $\"cos%28%283%2F2%29pi%29-sin%28%283%2F2%29pi%29%3E0\"$
\n" ); document.write( " $\"0-%28-1%29%3E0\"$
\n" ); document.write( " $\"1%3E0\"$
\n" ); document.write( "True.
\n" ); document.write( "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.
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