Precalculus Examples

$f (x) = \frac{3 x^{3} + 30}{2 x^{3}}$

Step 1

Set the denominator in $\frac{3 x^{3} + 30}{2 x^{3}}$ equal to $0$ to find where the expression is undefined.

$2 x^{3} = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Divide each term in $2 x^{3} = 0$ by $2$ and simplify.

Tap for more steps...

Step 2.1.1

Divide each term in $2 x^{3} = 0$ by $2$ .

$\frac{2 x^{3}}{2} = \frac{0}{2}$

Step 2.1.2

Simplify the left side.

Tap for more steps...

Step 2.1.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.2.1.1

Cancel the common factor.

$\frac{2 x^{3}}{2} = \frac{0}{2}$

Step 2.1.2.1.2

Divide $x^{3}$ by $1$ .

$x^{3} = \frac{0}{2}$

Step 2.1.3

Simplify the right side.

Tap for more steps...

Step 2.1.3.1

Divide $0$ by $2$ .

$x^{3} = 0$

Step 2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{0}$

Step 2.3

Simplify $\sqrt[3]{0}$ .

Tap for more steps...

Step 2.3.1

Rewrite $0$ as $0^{3}$ .

$x = \sqrt[3]{0^{3}}$

Step 2.3.2

Pull terms out from under the radical, assuming real numbers.

$x = 0$

Step 3

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

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0}$

Step 4