Find the Domain y = square root of 7x-4

$y = \sqrt{7 x - 4}$

Step 1

Set the radicand in $\sqrt{7 x - 4}$ greater than or equal to $0$ to find where the expression is defined.

$7 x - 4 \geq 0$

Step 2

Solve for $x$ .

Add $4$ to both sides of the inequality.

$7 x \geq 4$

Divide each term in $7 x \geq 4$ by $7$ and simplify.

Divide each term in $7 x \geq 4$ by $7$ .

$\frac{7 x}{7} \geq \frac{4}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} \geq \frac{4}{7}$

Divide $x$ by $1$ .

$x \geq \frac{4}{7}$

Step 3

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

Interval Notation:

$[\frac{4}{7}, \infty)$

Set-Builder Notation:

${x | x \geq \frac{4}{7}}$

Step 4