Precalculus Examples

$\sqrt{(3 x + 1) - 4}$

Step 1

Set the radicand in $\sqrt{(3 x + 1) - 4}$ greater than or equal to $0$ to find where the expression is defined.

$(3 x + 1) - 4 \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $4$ from $1$ .

$3 x - 3 \geq 0$

Step 2.2

Add $3$ to both sides of the inequality.

$3 x \geq 3$

Step 2.3

Divide each term in $3 x \geq 3$ by $3$ and simplify.

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Step 2.3.1

Divide each term in $3 x \geq 3$ by $3$ .

$\frac{3 x}{3} \geq \frac{3}{3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{3}{3}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{3}{3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $3$ by $3$ .

$x \geq 1$

Step 3

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

Interval Notation:

$[1, \infty)$

Set-Builder Notation:

${x | x \geq 1}$

Step 4