Question 85212: Please help
For the following equation, find the interval(s) where f(x),0. f(x)= (1)/(x^2-2x-8)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find the interval(s) where f(x) < 0
f(x) = 1/(x^2-2x-8) < 0
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Rewrite as:
f(x) < 1/[(x-4)(x+2)] < 0
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f(x) is undefined for x=-2 and x=4
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Draw a number line and label appropriate points x=-2 and x=4
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This divides the number line into three intervals.
Check a test value in each interval to see where the INEQUALITIES solutions lie.
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Interval(-inf,-2); test point x=-100; f(-100)=1/[(-)(-)] >0 so no solutions here
Interval (-2,4); test pt. x=0; f(0)=1/[(-)(+)] <0 so solutions here
Interval (4,inf); test pt.x=100; f(100)/1/(+)(+)] so no solutions here
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Final Answer:
-2 less x less than 4
or (-2,4)
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