document.write( "Question 869249: Determine the set of points where f (x) ≥ g (x), if f (x) = x2 – 4x and g (x) = x – 6. You may solve this either algebraically or graphically by graphing calculator. \n" ); document.write( "

Algebra.Com's Answer #524258 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
First find the points where the functions cross each other.
\n" ); document.write( " $\"f%28x%29=g%28x%29\"$
\n" ); document.write( " $\"x%5E2-4x=x-6\"$
\n" ); document.write( " $\"x%5E2-5x%2B6=0\"$
\n" ); document.write( " $\"%28x-2%29%28x-3%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"x-2=0\"$
\n" ); document.write( " $\"x=2\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x-3=0\"$
\n" ); document.write( " $\"x=3\"$
\n" ); document.write( "So break up the number line into three regions and test the inequality.
\n" ); document.write( " $\"x%3C2\"$
\n" ); document.write( " $\"x=0\"$
\n" ); document.write( " $\"0-4%3E0-6\"$
\n" ); document.write( " $\"-4%3E-6\"$
\n" ); document.write( "True
\n" ); document.write( " $\"2%3Cx%3C3\"$
\n" ); document.write( " $\"x=5%2F2\"$
\n" ); document.write( " $\"%285%2F2%29%5E2-4%285%2F2%29%3E5%2F2-6\"$
\n" ); document.write( " $\"25%2F4-20%2F2%3E5%2F2-12%2F2\"$
\n" ); document.write( " $\"25%2F4-40%2F4%3E-7%2F2\"$
\n" ); document.write( " $\"-15%2F4%3E-14%2F4\"$
\n" ); document.write( "False
\n" ); document.write( " $\"x%3E3\"$
\n" ); document.write( " $\"x=4\"$
\n" ); document.write( " $\"4%5E2-4%284%29%3E4-6\"$
\n" ); document.write( " $\"0%3E-2\"$
\n" ); document.write( "True
\n" ); document.write( "So now put it all together.
\n" ); document.write( "( $\"-infinity\"$ , $\"2\"$ ]U[ $\"3\"$ , $\"infinity\"$ )
\n" ); document.write( " \n" ); document.write( "

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