find the equation of the inverse function of g(x)=4(x-1)^2+8

g(x)=4(x-1)^2 + 8

let y = g(x)

y = 4(x-1)^2 + 8

y - 8 = 4(x-1)^2

(y-8)/4 = (x-1)^2

Sqrt[(y-8)/4] = x-1

x = Sqrt[(y-8) / 4] +1

replace x , y

y = Sqrt[(x-8) / 4]

g^-1(x) = Sqrt[(y-8) / 4] + 1

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