Question 342655
{{{f(s)=sqrt((s-1)/(s-4))}}}
Arguments for the square root function must be non-negative.
{{{(s-1)/(s-4)>=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}}}
{{{(s-1)/(s-4)>=0}}}
{{{(-1)/(-4)>=0}}}
{{{1/4>=0}}}
True, this region is part of the solution region.
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Region 2:{{{s=2}}}
{{{(s-1)/(s-4)>=0}}}
{{{(2-1)/(2-4)>=0}}}
{{{1/(-2)>=0}}}
{{{-(1/2)>=0}}}
False, this region is part of the solution region.
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Region 1:{{{s=5}}}
{{{(s-1)/(s-4)>=0}}}
{{{(5-1)/(5-4)>=0}}}
{{{4/1>=0}}}
{{{4>=0}}}
True, this region is part of the solution region.
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Domain:({{{-infinity}}},{{{1}}}]U({{{4}}},{{{infinity}}})