SOLUTION: find the interval(s) for the equation f(x)=1/x^2-2x-8, where f(x)>0

Question 114553: find the interval(s) for the equation f(x)=1/x^2-2x-8, where f(x)>0
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
For f(x) to be positive, the denominator has to stay greater than zero.

You can factor the denominator,

The zeros are then x=-2 and x=4.
Let's break up the problem into three parts
1.
2.
3.
That then covers the entire number line.
Let's look at each region,
1.

Negative times a negative equals a positive.
f(x) is positive when .
2.

Positive times a positive equals a positive.
f(x) is positive when .
3.

Negative times a positive equals a negative.
f(x) is negative when .
The interval where f(x) is positive is () and ().

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