SOLUTION: find the domain of the function: f(s)= the square root of s-1/s-4

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Question 342655: find the domain of the function: f(s)= the square root of s-1/s-4
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28s%29=sqrt%28%28s-1%29%2F%28s-4%29%29
Arguments for the square root function must be non-negative.
%28s-1%29%2F%28s-4%29%3E=0
Break up the number line into three regions.
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Region 1:(-infinity,1]
Region 2:[1,4)
Region 3:(4,infinity)
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x=1 is allowed, x=4 is not allowed since the function is undefined.
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Choose a point in each region (not an endpoint).
Test the inequality.
If the inequality is satisifed, the region is part of the solution.
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Region 1:s=0
%28s-1%29%2F%28s-4%29%3E=0
%28-1%29%2F%28-4%29%3E=0
1%2F4%3E=0
True, this region is part of the solution region.
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Region 2:s=2
%28s-1%29%2F%28s-4%29%3E=0
%282-1%29%2F%282-4%29%3E=0
1%2F%28-2%29%3E=0
-%281%2F2%29%3E=0
False, this region is part of the solution region.
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Region 1:s=5
%28s-1%29%2F%28s-4%29%3E=0
%285-1%29%2F%285-4%29%3E=0
4%2F1%3E=0
4%3E=0
True, this region is part of the solution region.
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Domain:(-infinity,1]U(4,infinity)