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.
Thanks
Answer by stanbon(75887)   (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.
|
|
|
