Precalculus Examples

$\sqrt{x - 7} + \sqrt{2 x}$

Step 1

Set the radicand in $\sqrt{x - 7}$ greater than or equal to $0$ to find where the expression is defined.

$x - 7 \geq 0$

Step 2

Add $7$ to both sides of the inequality.

$x \geq 7$

Step 3

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

$2 x \geq 0$

Step 4

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

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $2$ .

$x \geq 0$

Step 5

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

Interval Notation:

$[7, \infty)$

Set-Builder Notation:

${x | x \geq 7}$

Step 6