Answer:
The inverse of [tex]2(x - 2)^2 = 8(7 + y)[/tex] is [tex]y=\sqrt{(4x+28)}+2[/tex]
Step-by-step explanation:
Given equation :[tex]2(x - 2)^2 = 8(7 + y)[/tex]
[tex]\Rightarrow \frac{2(x-2)^2}{8}=7+y\\\Rightarrow \frac{2(x-2)^2}{8}-7=y[/tex]
Replace x with y and y with x
So, [tex]\Rightarrow \frac{2(y-2)^2}{8}-7=x\\\Rightarrow \frac{2(y-2)^2}{8}=x+7\\\Rightarrow 2(y-2)^2=8(x+7)\\\Rightarrow (y-2)^2=4(x+7)\\\Rightarrow (y-2)=\sqrt{4(x+7)}\\\Rightarrow y=\sqrt{4(x+7)}+2\\\Rightarrow y=\sqrt{4x+28)}+2[/tex]
So, Option C is correct
Hence The inverse of [tex]2(x - 2)^2 = 8(7 + y)[/tex] is [tex]y=\sqrt{(4x+28)}+2[/tex]
