Find the Domain of the Quotient of the Two Functions f(x) = square root of x , g(x)=x+9

$f (x) = \sqrt{x}$ , $g (x) = x + 9$

Step 1

Replace the function designators with the actual functions in $\frac{f (x)}{g (x)}$ .

$\frac{\sqrt{x}}{x + 9}$

Step 2

Set the radicand in $\sqrt{x}$ greater than or equal to $0$ to find where the expression is defined.

$x \geq 0$

Step 3

Set the denominator in $\frac{\sqrt{x}}{x + 9}$ equal to $0$ to find where the expression is undefined.

$x + 9 = 0$

Step 4

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 5

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 6