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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?

 Apr 6, 2021
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Hello @Skykeeper42! Welcome to this forum!

 

 

Multiplying the second equation by $2$, we get $4y=f(2x)+4$. So, because $(9,7)$ is on the graph of f(x), $x=\frac{9}{2}$ must be on the x graph of $4y=f(2x)+4$.

 

Now, just plug it in, and we get $f(2\frac{9}{2})=f(9)=7$, so $4y=7+2$, or $4y=9$, so $y=\frac{9}{4}$.

 

Now, summing up $\frac{9}{2}+\frac{9}{4}=\boxed{\frac{27}{4}}$

 Apr 6, 2021

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