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# Function

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Find the smallest integer x where the expression sqrt (x+8)/(x^2+x+16) is defined.

Oct 25, 2022

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The expression $$\dfrac{\sqrt{x+8}}{x^2+x+16}$$ is defined if:

$$x+8\ge 0 \implies x\ge -8$$

AND

$$x^2+x+16 \neq 0 \\ \text{Which, in real numbers, is already satisified; as it only equals 0 if x is a complex number.}$$

So the smallest x for which this expression is defined is -8.

Oct 25, 2022