What is the inverse of f(x)=(1/2 x-1)^2-2 ?

The inverse of f(x)=(1/2 x-1)^2-2 is 2sqrt(x+2)+2,-2sqrt(x+2)+2

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inverse of f(x)=(1/2 x-1)^2-2

inverse

f (x) = (\frac{1}{2} x - 1)^{2} - 2

2 x + 2 + 2, - 2 x + 2 + 2

Solution steps

y = (\frac{1}{2} x - 1)^{2} - 2

Replace

x

with

y

x = (\frac{1}{2} y - 1)^{2} - 2

Solve for

y, x = (\frac{1}{2} y - 1)^{2} - 2

2 x + 2 + 2, - 2 x + 2 + 2

What is the inverse of f(x)=(1/2 x-1)^2-2 ?
The inverse of f(x)=(1/2 x-1)^2-2 is 2sqrt(x+2)+2,-2sqrt(x+2)+2