Finite Math Examples

$f (x) = \sqrt{14 - 3 x}$

Step 1

Find the domain to determine if the expression is continuous.

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Step 1.1

Set the radicand in $\sqrt{14 - 3 x}$ greater than or equal to $0$ to find where the expression is defined.

$14 - 3 x \geq 0$

Step 1.2

Solve for $x$ .

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Step 1.2.1

Subtract $14$ from both sides of the inequality.

$- 3 x \geq - 14$

Step 1.2.2

Divide each term in $- 3 x \geq - 14$ by $- 3$ and simplify.

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Step 1.2.2.1

Divide each term in $- 3 x \geq - 14$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \leq \frac{- 14}{- 3}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} \leq \frac{- 14}{- 3}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 14}{- 3}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Dividing two negative values results in a positive value.

$x \leq \frac{14}{3}$

Step 1.3

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

Interval Notation:

$(- \infty, \frac{14}{3}]$

Set-Builder Notation:

${x | x \leq \frac{14}{3}}$

Interval Notation:

$(- \infty, \frac{14}{3}]$

Set-Builder Notation:

${x | x \leq \frac{14}{3}}$

Step 2

The expression is continuous.

Continuous

Step 3