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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?

 Oct 9, 2019
 #1
avatar+109563 
+2

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

 

 

cool cool cool

 Oct 9, 2019
 #2
avatar+108732 
+2

I got the same answer as Chris,


\(7=f(9)\\ 7=f(2*4.5)\\ \text{So if }x=4.5,  f(2x)=7\\\)

 

\(2y=\frac{f(2x)}{2}+2\\ When \;\;x=4.5\\ 2y=\frac{7}{2}+2\\ y=\frac{7}{4}+1\\ y=1\frac{3}{4}+1\\ y=2\frac{3}{4}\\ \text{So one point on the graph is }(4\frac{1}{2},2\frac{3}{4})\\~\\ \text{The sum of the coordinates is } 7\frac{1}{4} \)

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 Oct 10, 2019
 #3
avatar+109563 
+1

Thanks, Melody    !!!!

 

 

cool cool cool

CPhill  Oct 10, 2019

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