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# help me

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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?

Dec 13, 2018

#1
+3580
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$$2y=\dfrac{f(2x)}{2}+2\\ y = \dfrac{f(2x)}{4}+1\\ f\left(2 \dfrac 9 2\right)=f(9)=7\\ y = \dfrac{7}{4}+1=\dfrac{11}{4}\\ (x,y) = \left(\dfrac 9 2,~\dfrac{11}{4}\right)$$

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

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Dec 13, 2018

#1
+3580
+2

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

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

Rom Dec 13, 2018