document.write( "Question 143553: Find the domain and Range
\n" ); document.write( "f (x)=square root x-3 divided by 6-3x \n" ); document.write( "

Algebra.Com's Answer #104506 by nabla(475) $\"\"$ $\"About$

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Squares need to be >=0. Thus
\n" ); document.write( "x-3>=0
\n" ); document.write( "Implies x must be >=3\r
\n" ); document.write( "\n" ); document.write( "We cannot divide by zero, thus 6-3x cannot =0.
\n" ); document.write( "Find where that is the case. 6=3x ->x=2
\n" ); document.write( "So we have x cannot be 2 and must be >=3.\r
\n" ); document.write( "\n" ); document.write( "We thus have the following domain in interval notation: [3, $\"infinity\"$ ).\r
\n" ); document.write( "\n" ); document.write( "Since the numerator will always be positive or =0, we need only look at the denominator and see that this will always be negative (because x>=3 this means 6-3x<-3) except when x=3 (which gives y=0).\r
\n" ); document.write( "\n" ); document.write( "We thus have the follow range in interval notation: ( $\"-infinity\"$ ,0]\r
\n" ); document.write( "\n" ); document.write( "I will plot the graph for you as a check:
\n" ); document.write( " $\"graph%28+300%2C+200%2C+2%2C+5%2C+-2%2C+2%2C+sqrt%28x-3%29%2F%286-3x%29+%29\"$ \n" ); document.write( "

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