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What is the smallest real number x in the domain of the function g(x) = sqrt((x + 3)^2 - (x - 8)^2)?

 Feb 12, 2021

Best Answer 

 #1
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We notice the value under the square root must be positive to be in the domain. So we have $(x+3)^2-(x-8)^2\geq0$. We see that after simplifying, $22x-55\geq0$, where the minimum of $x$ is then $2.5$. Clearly, the smallest $x$ in the domain is $2.5$.

 Feb 12, 2021
 #1
avatar+62 
+3
Best Answer

We notice the value under the square root must be positive to be in the domain. So we have $(x+3)^2-(x-8)^2\geq0$. We see that after simplifying, $22x-55\geq0$, where the minimum of $x$ is then $2.5$. Clearly, the smallest $x$ in the domain is $2.5$.

CitrusCornflakes Feb 12, 2021

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