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

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

Step 1

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

$12 - 3 x \geq 0$

Step 2

Solve for $x$ .

Subtract $12$ from both sides of the inequality.

$- 3 x \geq - 12$

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

Divide each term in $- 3 x \geq - 12$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \leq \frac{- 12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \leq \frac{- 12}{- 3}$

Divide $x$ by $1$ .

$x \leq \frac{- 12}{- 3}$

Simplify the right side.

Divide $- 12$ by $- 3$ .

$x \leq 4$

Step 3

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

Interval Notation:

$(- \infty, 4]$

Set-Builder Notation:

${x | x \leq 4}$

Step 4

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

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