Question 72403: if f(x) = x(x+3)(x-1), use interval notation to give all values of x where
f(x)>0.
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! if f(x) = x(x+3)(x-1), use interval notation to give all values of x where
f(x)>0.
To find the possible intervals, set each term equal to 0 and solve for x:
x=0 or x+3=0 or x-1=0
x=0 or x+3-3=0-3 or x-1+1=0+1
x=0 or x=-3 or x=1
The possible intervals are (-infinity,-3) or (-3,0) or (0,1) or (1,infinity).
:
For (-infinity,-3), let x=-4 and see if the outcome is positive (>0).
f(-4)=-4(-4+3)(-4-1)=-4(-1)(-5)=-20 This interval is NOT >0.
:
For (-3,0), let x=-1
f(-1)=-1(-1+3)(-1-1)=-1(2)(-2)=4 This interval IS >0.
:
For (0,1), let x=.5
f(.5)=.5(.5+3)(.5-1)=.5(3.5)(-5.)=-.875 This interval is NOT >0.
:
For (1,infinity) let x=2
f(2)=2(2+3)(2-1)=2(5)(1)=10 This interval IS >0.
:
Therefore the solution is: (-3,0)U(1,infinity)
Happy Calculating!!!!!
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