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.
Subtract from to get .
Subtract from to get .

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Rewrite the equation as .
Add to both sides of the equation.
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 .
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