# Algebra 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

Subtract from .

Step 4

Subtract from .

Step 5

Step 5.1

Rewrite the equation as .

Step 5.2

Add to both sides of the equation.

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