Precalculus Examples

$\sqrt{13 - (13 - 2 x)}$

Step 1

Set the radicand in $\sqrt{13 - (13 - 2 x)}$ greater than or equal to $0$ to find where the expression is defined.

$13 - (13 - 2 x) \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Simplify $13 - (13 - 2 x)$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$13 - 1 \cdot 13 - (- 2 x) \geq 0$

Step 2.1.1.2

Multiply $- 1$ by $13$ .

$13 - 13 - (- 2 x) \geq 0$

Step 2.1.1.3

Multiply $- 2$ by $- 1$ .

$13 - 13 + 2 x \geq 0$

Step 2.1.2

Simplify by subtracting numbers.

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Step 2.1.2.1

Subtract $13$ from $13$ .

$0 + 2 x \geq 0$

Step 2.1.2.2

Add $0$ and $2 x$ .

$2 x \geq 0$

Step 2.2

Divide each term in $2 x \geq 0$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 x \geq 0$ by $2$ .

$\frac{2 x}{2} \geq \frac{0}{2}$

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.

$\frac{2 x}{2} \geq \frac{0}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{0}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $0$ by $2$ .

$x \geq 0$

Step 3

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 4