# 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:

Raise to the power of .

Raise to the power of .

Rewrite the equation as .

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

Simplify .

Rewrite as .

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

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 .