1. ## Intermediate Value Theorem

Need some help.
Suppose that f: [0,2] -> [0,4] is continuous. Use the IVT to show that there is an x in [0.2] such that f(x)=2x.

Was given this hint to try and use g: [0,2] -> R defined by g(x)= f(x)-2x. this doesn't seem to help me much.

Any help would be greatly appreciated!

2. $\displaystyle g(0)\ge 0\ge g(2)$ Is this correct?
Does that imply $\displaystyle \left( {\exists a \in [0,2]} \right)\left[ {g(a) = 0} \right]?$
Does that help?