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

The inverse of 1/2 ln(x^2-2x-1) is 1+sqrt(e^{2x)+2},1-sqrt(e^{2x)+2}

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inverse of 1/2 ln(x^2-2x-1)

inverse

\frac{1}{2} ln (x^{2} - 2 x - 1)

1 + e^{2 x} + 2, 1 - e^{2 x} + 2

Solution steps

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

Replace

x

with

y

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

Solve for

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

1 + e^{2 x} + 2, 1 - e^{2 x} + 2

What is the inverse of 1/2 ln(x^2-2x-1) ?
The inverse of 1/2 ln(x^2-2x-1) is 1+sqrt(e^{2x)+2},1-sqrt(e^{2x)+2}