|$2x + 1 = 2$
$ \ \ \ \ -1 = -1$
$2x\ \ \ \ \ = 1$
$\frac 12 (2x) = \frac 12 (1)$
$\ \ \ \ \ x = \frac 12$
|Check the box in the GeoGebra sketch to see a visualization of the solution.
||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 $x=\frac 12$, $f(x) = s(m(\frac 12))=s(1)=2$
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 equations $Ax + B = C$ are solved visually with the mapping diagram.