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asambeis [7]
3 years ago
10

How do find the domain and range of

le="\frac{1}{\sqrt{x-8}}" alt="\frac{1}{\sqrt{x-8}}" align="absmiddle" class="latex-formula">?
Mathematics
1 answer:
Kisachek [45]3 years ago
3 0
\sqrt{x-8} is undefined if the argument x-8 is negative, so you first need to require that

x-8\ge0\implies x\ge8

We're not done yet, though, because \dfrac1{\sqrt{x-8}} still doesn't exist when x=8, so we remove this from the domain and we're left with x>8, or in interval notation, (8,\infty)

To find the range, consider the limits of the function as you approach either endpoint of the domain.

\displaystyle\lim_{x\to8^+}\frac1{\sqrt{x-8}}=+\infty
\displaystyle\lim_{x\to\infty}\frac1{\sqrt{x-8}}=0

Since \dfrac1{\sqrt{x-8}} is positive everywhere, the range is (0,\infty)
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grandymaker [24]
Just subtract but take care of the power or else you can come up with wrong results !

so first make the power same ;

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so now subtract = (18.98-5.68) × 10(26)
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