Precalculus Examples

$f (x) = \sqrt{2 x - 8}$

Step 1

Set the radicand in $\sqrt{2 x - 8}$ greater than or equal to $0$ to find where the expression is defined.

$2 x - 8 \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $8$ to both sides of the inequality.

$2 x \geq 8$

Step 2.2

Divide each term in $2 x \geq 8$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 x \geq 8$ by $2$ .

$\frac{2 x}{2} \geq \frac{8}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{8}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{8}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $8$ by $2$ .

$x \geq 4$

Step 3

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

Interval Notation:

$[4, \infty)$

Set-Builder Notation:

${x | x \geq 4}$

Step 4