[tex]\bf \begin{cases}
f(x)\qquad (\stackrel{x}{5},\stackrel{y}{2})\\\\
g(x)=3f(x+7)
\end{cases}[/tex]
if we substitute "x" for "x+7", that's is just a horizontal shift of 7 units, to the left, so the x-coordinate in f(x) of 5, will move 7 units to the left then, or 5 - 7 = -2.
now, the point itself has moved horizontally 7 units, that means the y-coordinate of 2 moved as well, 2 - 7 = -5.
so the new location for 5,2 is at -2, -5.
then the "3" shrinkage,
3(-2) = -6 <---- x-coordinate,
and 3(-5) = -15 <---- y-coordinate
so, the new location for 5,2 with the translations in g(x), is at (-6, -15)
