SOLUTION: All sqaure root x-2 over x-1 find domain my answer is [2, positive infite) I am right that answer

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Question 342768: All sqaure root x-2 over x-1 find domain
my answer is [2, positive infite) I am right that answer
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
No, not completely.
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The square root function needs a non-negative argument.
%28%28x-2%29%2F%28x-1%29%29%3E=0
Break up the number line into 3 regions.
Region 1:(-infinity,1)
Region 2:(1,2)
Region 3:(2,infinity)
Choose a point in the region, not an endpoint.
Test the inequality.
If the inequality is satisfied, the region is part of the solution.
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Region 1: x=0
%28x-2%29%2F%28x-1%29%3E=0
-2%2F-1%3E=0
2%3E=0
True, this region is part of the solution.
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Region 2: x=3%2F2
%28x-2%29%2F%28x-1%29%3E=0
%283%2F2-2%29%2F%283%2F2-1%29%3E=0
-%281%2F2%29%2F%281%2F2%29%3E=0
-1%3E=0
False, this region is not part of the solution.
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Region 3: x=3
%28x-2%29%2F%28x-1%29%3E=0
%283-2%29%2F%283-1%29%3E=0
1%2F2%3E=0
True, this region is part of the solution.
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Since x=2 also solves the inequality, it is also included.
x=1 is not included in any solution region because it leads to a division by zero.
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Domain:(-infinity,1) U [2,infinity)