# Another Analysis question: continuity and compactness

by TaylorWatts
Tags: analysis, compactness, continuity
 P: 367 Consider the function $g : I \to \mathbb{R}$ given by $g \left( x \right) = f \left( x \right) - x$. What happens if $g \left( x \right) = 0$ for some $x$? How can you show that this has to happen in $I$? I'm sure you must know a nice theorem that you can use here.