# SOLUTION: For the following equation, find the interval(s) where f(x) < 0 f(x) = 1/(x^2-2x-8) (–4, 2) (–2, 4) (2, 4) (2, 8) I can't figure this one out. I know it's probly easy

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: For the following equation, find the interval(s) where f(x) < 0 f(x) = 1/(x^2-2x-8) (–4, 2) (–2, 4) (2, 4) (2, 8) I can't figure this one out. I know it's probly easy       Log On

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 Click here to see ALL problems on Trigonometry-basics Question 85223: For the following equation, find the interval(s) where f(x) < 0 f(x) = 1/(x^2-2x-8) (–4, 2) (–2, 4) (2, 4) (2, 8) I can't figure this one out. I know it's probly easy for most but assistance would be great. ThanksAnswer by stanbon(57967)   (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 ----------------- Rewrite as: f(x) < 1/[(x-4)(x+2)] < 0 --------- f(x) is undefined for x=-2 and x=4 ----------- Draw a number line and label appropriate points x=-2 and x=4 -------------- This divides the number line into three intervals. Check a test value in each interval to see where the INEQUALITIES solutions lie. -------------- 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 ----------------- Final Answer: -2 less x less than 4 or (-2,4) ========================== Cheers, Stan H.