# Finite Math Examples

,

Step 1

The Intermediate Value Theorem states that, if is a real-valued continuous function on the interval , and is a number between and , then there is a contained in the interval such that .

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

Set-Builder Notation:

Step 3

Step 3.1

Simplify each term.

Step 3.1.1

Raising to any positive power yields .

Step 3.1.2

Multiply by .

Step 3.2

Simplify by adding and subtracting.

Step 3.2.1

Add and .

Step 3.2.2

Subtract from .

Step 4

Step 4.1

Simplify each term.

Step 4.1.1

Raise to the power of .

Step 4.1.2

Multiply by .

Step 4.2

Simplify by adding and subtracting.

Step 4.2.1

Add and .

Step 4.2.2

Subtract from .

Step 5

Graph each side of the equation. The solution is the x-value of the point of intersection.

Step 6

The Intermediate Value Theorem states that there is a root on the interval because is a continuous function on .

The roots on the interval are located at .

Step 7