SOLUTION: For f(x)= 1/x^2-2x-8, find the intervals where f(x)<0

Question 82590This question is from textbook
: For f(x)= 1/x^2-2x-8, find the intervals where f(x)<0 This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
For f(x)= 1/x^2-2x-8, find the intervals where f(x)<0
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f(x) = 1/[(x-4)(x+2)]
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Comment: f(x) has vertical asymptotes at x=-2 and x=4
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Draw a number line and mark appropriate points as x=-2 and as x=4.
That breaks the line into three intervals. Check a point in each
interval to see where the solution intervals for your equation lie.
Check (-inf,-2): pick x=100, then f(-100)=1/(-)(-)>0; no solutions there.
Check (-2,4); pick x=0, then f(0) = 1/(-)(+)<0; solution here.
Check (4,inf); pick x=100; then f(100)= 1/(+)(+); no solutions there.
The solution is all vales of x between x=-2 and x=4 but not including
x=-2 and x=4.
Interval notation solution: (-2,4)
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Cheers,
Stan H.
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