# Algebra Examples

,

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 .

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:

Simplify each term.

Raising to any positive power yields .

Multiply by .

Simplify by adding and subtracting.

Add and .

Subtract from .

Simplify each term.

Raise to the power of .

Multiply by .

Simplify by adding and subtracting.

Add and .

Subtract from .

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

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 .