document.write( "Question 114553: find the interval(s) for the equation f(x)=1/x^2-2x-8, where f(x)>0 \n" ); document.write( "

Algebra.Com's Answer #83352 by Fombitz(32388) $\"\"$ $\"About$

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For f(x) to be positive, the denominator has to stay greater than zero.
\n" ); document.write( " $\"x%5E2-2x-8%3E0\"$
\n" ); document.write( "You can factor the denominator,
\n" ); document.write( " $\"x%5E2-2x-8=%28x-4%29%28x%2B2%29\"$
\n" ); document.write( "The zeros are then x=-2 and x=4.
\n" ); document.write( "Let's break up the problem into three parts
\n" ); document.write( "1. $\"x%3C-2\"$
\n" ); document.write( "2. $\"x%3E4\"$
\n" ); document.write( "3. $\"-2%3Cx%3C4\"$
\n" ); document.write( "That then covers the entire number line.
\n" ); document.write( "Let's look at each region,
\n" ); document.write( "1. $\"x%3C-2\"$
\n" ); document.write( " $\"%28x-4%29%3C0\"$
\n" ); document.write( " $\"%28x%2B2%29%3C0\"$
\n" ); document.write( "Negative times a negative equals a positive.
\n" ); document.write( "f(x) is positive when $\"x%3C-2\"$ .
\n" ); document.write( "2. $\"x%3E4\"$
\n" ); document.write( " $\"%28x-4%29%3E0\"$
\n" ); document.write( " $\"%28x%2B2%29%3E0\"$
\n" ); document.write( "Positive times a positive equals a positive.
\n" ); document.write( "f(x) is positive when $\"x%3E4\"$ .
\n" ); document.write( "3. $\"-2%3Cx%3C4\"$
\n" ); document.write( " $\"%28x-4%29%3C0\"$
\n" ); document.write( " $\"%28x%2B2%29%3E0\"$
\n" ); document.write( "Negative times a positive equals a negative.
\n" ); document.write( "f(x) is negative when $\"-2%3Cx%3C4\"$ .
\n" ); document.write( "The interval where f(x) is positive is ( $\"x%3C-2\"$ ) and ( $\"x%3E4\"$ ).
\n" ); document.write( " \n" ); document.write( "

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