Find the Domain of the Product f(x)=6x+5 , g(x) = square root of x

$f (x) = 6 x + 5$ , $g (x) = \sqrt{x}$

Find the product of the functions.

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

$(6 x + 5) \cdot (\sqrt{x})$

Apply the distributive property.

$6 x \sqrt{x} + 5 \sqrt{x}$

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

$x \geq 0$

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Find the Domain of the Product f(x)=6x+5 , g(x) = square root of x

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