Finite Math Examples

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

Step 1

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{x^{3}}$

Step 2

Set the radicand in $\sqrt{x^{3}}$ less than $0$ to find where the expression is undefined.

$x^{3} < 0$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

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

Step 3.2

Simplify the equation.

Tap for more steps...

Step 3.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.1.1

Pull terms out from under the radical.

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

Step 3.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.1

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

Tap for more steps...

Step 3.2.2.1.1

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

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

Step 3.2.2.1.2

Pull terms out from under the radical.

$x < 0$

Step 4

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x < 0$

$(- \infty, 0)$

Step 5