# Sets : Intermediate Value Theorem

Prove that the interval (0,2)~R.

Use the Intermediate Value Theorem.

https://brainmass.com/math/calculus-and-analysis/sets-intermediate-value-theorem-11824

#### Solution Preview

To solve this, we consdier the function:

f(x)=rx-r

where r is a positive real number (i.e. r is in R)

When x=0, we have f(0)=-r

When x=2, we have ...

#### Solution Summary

The Intermediate Value Theorem is used to prove that the interval (0,2)~R.

$2.19