Question 7537: For f(x)=1/x^2-2x-8 , find the interval(s) where f(x) < 0.
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! At first, two big mistakes you did:
(I)wrong cateory posting
(II) missing parenthesis
Be careful!!!
f(x)=1/(x^2-2x-8) <0 is equivalent to x^2-2x-8 <0 [since 1 is positive.]
Solve x^2-2x-8 = (x - 4)(x+2) < 0.
[Note two roots 4 & -2 divide the whole real line ibnto 3 parts]
From the signs in diagram below:
+ - +
---------*--------*----------
-2 4
The solution set : (-2, 4)
Here,I give you the simplest way to solve this kind of questions.
Try to read and think carefully about every step.
No further explanations will be given.
Kenny
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