Find the Domain f(x) = square root of 6x-42

$f (x) = \sqrt{6 x - 42}$

Set the radicand in $\sqrt{6 x - 42}$ greater than or equal to $0$ to find where the expression is defined.

$6 x - 42 \geq 0$

Solve for $x$ .

Add $42$ to both sides of the inequality.

$6 x \geq 42$

Divide each term in $6 x \geq 42$ by $6$ and simplify.

Divide each term in $6 x \geq 42$ by $6$ .

$\frac{6 x}{6} \geq \frac{42}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} \geq \frac{42}{6}$

Divide $x$ by $1$ .

$x \geq \frac{42}{6}$

Simplify the right side.

Divide $42$ by $6$ .

$x \geq 7$

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

Interval Notation:

$[7, \infty)$

Set-Builder Notation:

${x | x \geq 7}$