Find the Domain of the Product of the Functions f(x)=2x+1 , g(x) = square root of x

$f (x) = 2 x + 1$ , $g (x) = \sqrt{x}$

Step 1

Find the product of the functions.

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

$(2 x + 1) \cdot (\sqrt{x})$

Simplify.

Apply the distributive property.

$2 x \sqrt{x} + 1 \sqrt{x}$

Multiply $\sqrt{x}$ by $1$ .

$2 x \sqrt{x} + \sqrt{x}$

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