# Algebra Examples

Prove that a Root is on the Interval
,
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:
Calculate .
Simplify each term.
Raising to any positive power yields .
Multiply by .
Subtract from .
Calculate .
Simplify each term.
Raise to the power of .
Multiply by .