To find the inverse of the given equation \(2(x-2)^2 = 8(7+y)\), we need to isolate \(y\) in terms of \(x\). Here’s a step-by-step process to do this:
1. Start with the given equation:
[tex]\[
2(x-2)^2 = 8(7+y)
\][/tex]
2. Divide both sides by 8 to simplify:
[tex]\[
\frac{2(x-2)^2}{8} = 7 + y
\][/tex]
[tex]\[
\frac{(x-2)^2}{4} = 7 + y
\][/tex]
3. Subtract 7 from both sides to isolate \(y\):
[tex]\[
\frac{(x-2)^2}{4} - 7 = y
\][/tex]
Thus, the equation for \(y\) in terms of \(x\) is:
[tex]\[
y = \frac{(x-2)2}{4} - 7
\][/tex]
From the options provided, the correct inverse equation is:
[tex]\[
\boxed{[(x - 2)^2/4 - 7]}
\][/tex]
