In the rectangular coordinate plane, the graphs of functions $\mathrm{f}(\mathrm{x})$ and $\mathrm{g}(\mathrm{x})$ defined on the interval $[0,3]$ are given in the figure.
For a number $\mathrm{a} \in (0,1)$,
$$\begin{aligned}
& \mathrm{b} = (f \circ g)(a) \\
& c = (g \circ f)(a)
\end{aligned}$$
are determined.
Accordingly, which of the following is the correct ordering of the numbers a, b, and c?
A) a $<$ b $<$ c
B) a $<$ c $<$ b
C) b $<$ a $<$ c
D) b $<$ c $<$ a
E) c $<$ a $<$ b