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 = f(2x) / 2 + 2 divide through by 2
y = (1/4) f(2x) + 1
The point (9/2, (1/4)(7) + 1) = (9/2, 7/4 + 1) = (9/2, 11/4) will be on the graph
The sum of the coordinates is 9/2 + 11/4 = 18/4 + 11/4 = 29/4
I got the same answer as Chris,
\(7=f(9)\\ 7=f(2*4.5)\\ \text{So if }x=4.5, f(2x)=7\\\)
\(2y=\frac{f(2x)}{2}+2\\ When \;\;x=4.5\\ 2y=\frac{7}{2}+2\\ y=\frac{7}{4}+1\\ y=1\frac{3}{4}+1\\ y=2\frac{3}{4}\\ \text{So one point on the graph is }(4\frac{1}{2},2\frac{3}{4})\\~\\ \text{The sum of the coordinates is } 7\frac{1}{4} \)