Find the Domain of the Sum of the 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 $f (x) + g (x)$ .

$\sqrt{x} + x - 9$

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

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 4