Find the Domain and Range f(x) = square root of 3x-12

$f (x) = \sqrt{3 x - 12}$

Set the radicand in $\sqrt{3 x - 12}$ greater than or equal to $0$ to find where the expression is defined.

$3 x - 12 \geq 0$

Solve for $x$ .

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Add $12$ to both sides of the inequality.

$3 x \geq 12$

Divide each term by $3$ and simplify.

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Divide each term in $3 x \geq 12$ by $3$ .

$\frac{3 x}{3} \geq \frac{12}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 x}{3} \geq \frac{12}{3}$

Divide $x$ by $1$ .

$x \geq \frac{12}{3}$

Divide $12$ by $3$ .

$x \geq 4$

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

Interval Notation:

$[4, \infty)$

Set-Builder Notation:

${x | x \geq 4}$

The range of an even indexed radical starts at its starting point $(4, 0)$ and extends to infinity.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${y | y \geq 0}$

Determine the domain and range.

Domain: $[4, \infty), {x | x \geq 4}$

Range: $[0, \infty), {y | y \geq 0}$

Find the Domain and Range f(x) = square root of 3x-12

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