Precalculus Examples

$f (x) = \sqrt{4 x - 9}$

Step 1

Set the radicand in $\sqrt{4 x - 9}$ greater than or equal to $0$ to find where the expression is defined.

$4 x - 9 \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $9$ to both sides of the inequality.

$4 x \geq 9$

Step 2.2

Divide each term in $4 x \geq 9$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 x \geq 9$ by $4$ .

$\frac{4 x}{4} \geq \frac{9}{4}$

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.

$\frac{4 x}{4} \geq \frac{9}{4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{9}{4}$

Step 3

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

Interval Notation:

$[\frac{9}{4}, \infty)$

Set-Builder Notation:

${x | x \geq \frac{9}{4}}$

Step 4