Precalculus Examples

$\sqrt{4 x - 2}$

Step 1

Set the radicand in $\sqrt{4 x - 2}$ greater than or equal to $0$ to find where the expression is defined.

$4 x - 2 \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $2$ to both sides of the inequality.

$4 x \geq 2$

Step 2.2

Divide each term in $4 x \geq 2$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 x \geq 2$ by $4$ .

$\frac{4 x}{4} \geq \frac{2}{4}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{2}{4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{2}{4}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Cancel the common factor of $2$ and $4$ .

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Step 2.2.3.1.1

Factor $2$ out of $2$ .

$x \geq \frac{2 (1)}{4}$

Step 2.2.3.1.2

Cancel the common factors.

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Step 2.2.3.1.2.1

Factor $2$ out of $4$ .

$x \geq \frac{2 \cdot 1}{2 \cdot 2}$

Step 2.2.3.1.2.2

Cancel the common factor.

$x \geq \frac{2 \cdot 1}{2 \cdot 2}$

Step 2.2.3.1.2.3

Rewrite the expression.

$x \geq \frac{1}{2}$

Step 3

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

Interval Notation:

$[\frac{1}{2}, \infty)$

Set-Builder Notation:

${x | x \geq \frac{1}{2}}$

Step 4