On the GeoGebra figures move the value of $x$ on the mapping diagram to explore the relation between the values of $f(x)$ (in blue) and $g(x)$ (in red) at $x= \frac 5 4$ and $x=4$..

For the graphs of $f$ and $g$:
Find the point(s) on the graph of $f$ and $g$ where the two
graphs intersect, determine the first coordinate, $4$, and
that is the desired value for $x$. |
For the mapping diagrams of
$f$ and $g$: Find the point(s) $x$ on the source
axis with a single function arrow pointing to $f(x) = g(x)$. |

Martin Flashman, 7 December 2013, Created with GeoGebra