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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the interval(s) for the equation f(x)=1/x^2-2x-8, where f(x)>0      Log On


   

Question 114553: find the interval(s) for the equation f(x)=1/x^2-2x-8, where f(x)>0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For f(x) to be positive, the denominator has to stay greater than zero.
x%5E2-2x-8%3E0
You can factor the denominator,
x%5E2-2x-8=%28x-4%29%28x%2B2%29
The zeros are then x=-2 and x=4.
Let's break up the problem into three parts
1. x%3C-2
2. x%3E4
3. -2%3Cx%3C4
That then covers the entire number line.
Let's look at each region,
1. x%3C-2
%28x-4%29%3C0
%28x%2B2%29%3C0
Negative times a negative equals a positive.
f(x) is positive when x%3C-2.
2.x%3E4
%28x-4%29%3E0
%28x%2B2%29%3E0
Positive times a positive equals a positive.
f(x) is positive when x%3E4.
3.-2%3Cx%3C4
%28x-4%29%3C0
%28x%2B2%29%3E0
Negative times a positive equals a negative.
f(x) is negative when -2%3Cx%3C4.
The interval where f(x) is positive is (x%3C-2) and (x%3E4).