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Question 51384: state the domain of:
G(x)=(x^2-x-6)^(1/2)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! state the domain of:
G(x)=(x^2-x-6)^(1/2)
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To get real number results x^2-x-6 must not be negative.
x^2-x-6>=0
(x-3)(x+2)>=0
Need to find the solution set.
Plot the zeroes, -2 and 3, on a number line.
Examine the intervals determined to find the rest of the solution set.
Interval I is (-infinity,-2); check x=-10: (-10-3)(-10+2)>0.
So Interval I is part of the solution set.
Interval II is (-2,3); check x=0: (0-3)(0+2)<0.
So INterval II is not part of the solution set.
Interval III is (3,infinity); check=10: (10-3)(10+2)>0
So interval III is part of the solution set.
DOMAIN: All Real Numbers except -2
Cheers,
stan H.
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