document.write( "Question 901641: what is the domain of the following function
\n" ); document.write( " f(x) = sqrt(((x^3)/3) - x)
\n" ); document.write( " a)(−infinite, -sqrt3]and[0, infinite)
\n" ); document.write( " b)[−sqrt3, 0]and[sqrt3, infinite)
\n" ); document.write( " c)[−sqrt3, sqrt3]
\n" ); document.write( " d)(−infinite, −sqrt3]and[sqrt3, infinite) \n" ); document.write( "

Algebra.Com's Answer #546875 by Fombitz(32388) $\"\"$ $\"About$

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The argument of the square root must be non-negative:
\n" ); document.write( " $\"graph%28300%2C300%2C-4%2C4%2C-4%2C4%2Cx%5E3%2F3-x%29\"$
\n" ); document.write( " $\"x%5E3%2F3-x%3E=0\"$
\n" ); document.write( " $\"x%28x%5E2%2F3-1%29%3E=0\"$
\n" ); document.write( "Critical points:
\n" ); document.write( " $\"x%5E2%2F3-1=0\"$
\n" ); document.write( " $\"x%5E2=3\"$
\n" ); document.write( " $\"x=0+%2B-+sqrt%283%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x=0\"$
\n" ); document.write( "So from the graph, it looks like, the regions where the function is non-negative are,
\n" ); document.write( "( $\"-sqrt%283%29\"$ , $\"0\"$ )U( $\"sqrt%283%29\"$ , $\"infinity\"$ )
\n" ); document.write( " \n" ); document.write( "

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