If $aI have the following GRE question that I have some trouble seeing. 
If $g$ is a function defined o the open interval $(a,b)$ such that $a < g(x) < x$ for all $x \in (a,b)$, then $g$ is 
A) an unbounded function
B) a nonconstant function
C) a nonnegative function
D) a strictly increasing function
E) a polynomial function of degee 1
I answered that D), because I thought I could take the derivative on the inequality $a < g(x) < x$ and get $0< g'(x)<1$, showing that the equation is strictly increasing. However the answer says it should be B) and I don't really see how they concluded this. Could anyone help me with this problem?
Thanks in advanced!

Differentiation is not monotonic, unlike integration.

GRE Subject Test in Mathematics - Where can I find related past papers, solutions to those, sample tests, advice, books, apps or other resources?
