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What is the smallest real number in the domain of the function g(x) = sqrt((x - 3)^2 - (x - 18)^2)?

 Jun 12, 2021
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The quantity inside square root must be non-negative for $g(x)$ to be a real-valued function.  This constraint $(x - 3)^2 - (x - 18)^2 \ge 0$ can be solved for $x$ to $x\ge 10.5$, so 10.5 is the desired minimum.
 

 Jun 12, 2021

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