Trigonometry Examples

$u (x) = \sqrt{8 x - 40}$

Step 1

Find the domain to determine if the expression is continuous.

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Step 1.1

Set the radicand in $\sqrt{8 x - 40}$ greater than or equal to $0$ to find where the expression is defined.

$8 x - 40 \geq 0$

Step 1.2

Solve for $x$ .

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Step 1.2.1

Add $40$ to both sides of the inequality.

$8 x \geq 40$

Step 1.2.2

Divide each term in $8 x \geq 40$ by $8$ and simplify.

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Step 1.2.2.1

Divide each term in $8 x \geq 40$ by $8$ .

$\frac{8 x}{8} \geq \frac{40}{8}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $8$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} \geq \frac{40}{8}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{40}{8}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $40$ by $8$ .

$x \geq 5$

Step 1.3

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

Interval Notation:

$[5, \infty)$

Set-Builder Notation:

${x | x \geq 5}$

Interval Notation:

$[5, \infty)$

Set-Builder Notation:

${x | x \geq 5}$

Step 2

The expression is continuous.

Continuous

Step 3