Question:
Given that the point $(4,7)$ is on the graph of $y=3f\left(2x\right)+1$, there is one point that must be on the graph of $y=f(x)$. What is the sum of coordinates of that point?

Answer:
Given that $(4,7)$ is on the graph of $y=3f\left(2x\right)+1$, we can substitute $x=4$ and $y=7$ in that equation to obtain $$7 = 3f\left(2\cdot4\right)+1.$$We can rewrite this information as $$2 = f(8),$$which tells us that $(8,2)$ must be on the graph of $y=f(x)$. The sum of coordinates of this point is $\boxed{10}$.