Given that the point \((9,7)\) is on the graph of \(y = f(x)\), there is one point that must be on the graph of \(2y=\frac{f(2x)}2+2\). What is the sum of coordinates of that point?

\(2y=\dfrac{f(2x)}{2}+2\\ y = \dfrac{f(2x)}{4}+1\\ f\left(2 \dfrac 9 2\right)=f(9)=7\\ y = \dfrac{7}{4}+1=\dfrac{11}{4}\\ (x,y) = \left(\dfrac 9 2,~\dfrac{11}{4}\right)\)

\(x+y = \dfrac{18+11}{4} = \dfrac{29}{4}\)