What is the inverse of f(x)=sqrt(2x-2)-4 ?

The inverse of f(x)=sqrt(2x-2)-4 is (x^2+8x+18)/2

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inverse of f(x)=sqrt(2x-2)-4

inverse

f (x) = 2 x - 2 - 4

\frac{x ^{2} + 8 x + 18}{2}

Solution steps

y = 2 x - 2 - 4

Replace

x

with

y

x = 2 y - 2 - 4

Solve for

y, x = 2 y - 2 - 4

\frac{x ^{2} + 8 x + 18}{2}

f (x) = - x^{2} + 4 x + 2

f (x) = 6 x + 2 - 15

f (x) = - 5 (x - 3)^{2} + 8

f (x) = \frac{x}{2} + \frac{1}{2}

f (x) = - 6 x + 4

What is the inverse of f(x)=sqrt(2x-2)-4 ?
The inverse of f(x)=sqrt(2x-2)-4 is (x^2+8x+18)/2