# Finite Math 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.
Calculate .
Remove parentheses around .
Raise to the power of to get .
Calculate .
Remove parentheses around .
Raise to the power of to get .
is not on the interval .
There is no root on the interval.