On the GeoGebra mapping diagram for the composition, find $2$ on the final target axis.
Undo $s$ by subtracting
$1$ from $2$. This corresponds to going back on the diagram from $2$ on the
final axis to $2-1=1$ on the middle axis, reversing the arrow that would go from $1$ to $2$ visualizing $s$.
Thus if $m(x) = 1$ then $f(x) =
s(m(x))=s(1)=2$
Undo $m$ by multiplying $1$ by $\frac 12$. This
corresponds to going back on
the diagram from $1$ on the middle axis to $\frac 12$ on the source
axis, reversing the arrow that would go from $\frac 12$ to $1$ visualizing $m$.
Thus when $x\le\frac 12$, $f(x) \le s(m(\frac
12))=s(1)=2$
On the GeoGebra sketch you can change the values of $m=A$ and $b=B$
(with the sliders) and $C$ (currently $2$ on the target axis) to see
other linear inequalities $Ax + B \le C$ are solved visually with the mapping
diagram.