Let $f (x) = x^{2}$ $f(x)=x^2$ and $g (x) = \sqrt{x}$ $g(x)=sqrtx$ , how do you find the domain and rules of $(\frac{f}{g}) (x)$ $(f/g)(x)$ ?

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Let $f (x) = x^{2}$ $f(x)=x^2$ and $g (x) = \sqrt{x}$ $g(x)=sqrtx$ , how do you find the domain and rules of $(\frac{f}{g}) (x)$ $(f/g)(x)$ ?

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Answer 1 · 2017-10-26T12:19:08

Domain: $x > 0$ $x > 0$
$(\frac{f}{g}) (x) = \sqrt{x^{3}} or, equivalently x^{\frac{3}{2}}$ $(f/g)(x)=sqrt(x^3)" or, equivalently "x^(3/2)$

Explanation:

$\frac{f (x)}{g (x)} = \frac{x^{2}}{\sqrt{x}}$ $(f(x))/(g(x))=(x^2)/sqrt(x)$ ...and since
$XXXXXX$ $color(white)("XXXXXX")$ division by zero is undefined, and
$XXXXXX$ $color(white)("XXXXXX")$ square root of negative numbers are not defined for Real values
$XXX$ $color(white)("XXX")$ we can eliminate any values of $x \leq 0$ $x <= 0$
leaving us with a domain of $x > 0$ $x > 0$

$\frac{x^{2}}{\sqrt{x}} = x^{2} \times x^{- \frac{1}{2}} = x^{\frac{3}{2}}$ $x^2/sqrt(x)=x^2xxx^(-1/2)=x^(3/2)$ or
$XXXXXXXXXX = {(\sqrt{x})}^{3}$ $color(white)("XXXXXXXXXX")=(sqrt(x))^3$ or
$XXXXXXXXXX = {\sqrt{x^{3}}}^{2}$ $color(white)("XXXXXXXXXX")=sqrt(x^3)^2$

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Let $f (x) = x^{2}$ $f(x)=x^2$ and $g (x) = \sqrt{x}$ $g(x)=sqrtx$ , how do you find the domain and rules of $(\frac{f}{g}) (x)$ $(f/g)(x)$ ?

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Let $f (x) = x^{2}$ $f(x)=x^2$ and $g (x) = \sqrt{x}$ $g(x)=sqrtx$ , how do you find the domain and rules of $(\frac{f}{g}) (x)$ $(f/g)(x)$ ?