Question 72589: I have checked all possible answers and heeeeeers my question. someone please explain how do I need to do this. You guys/gals are all I have in helping me.
for f(x) = 1/x^2 -2x -8, find the interval(s) where f(x) < 0.
-4, 2
-2, 4
2, 4
2, 8
Thank you if you can take the time to teach me.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! f(x) = 1/x^2 -2x -8, find the interval(s) where f(x) < 0.
f(x) = 1/[(x-4)(x-2)]
F(x) will be<0 when [(x-4)(x-2)] is less than zero and x is not 2 or 4.
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When is (x-4)(x-2)<0 ??
Draw a number line and mark x=2 and x=4 on it.
That establishes three intervals.
Find the intervals which make (x-4)(x-2)<0
Check interval (-inf,2); select x=-100; you get (100-4)(100-2)>0 Therefore
the interval is NOT part of the solution.
Check interval (2.4); select x=3; you get (3-4)(3-2)<0 Therefore the
interval is part of the solution.
Check interval (4,inf); select x=100; you get (100-4)(100-2)>0 Therefore
the interval is NOT part of the solution.
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Solution summary: (2,4)
Cheers,
Stan H.
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