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

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

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inverse of f(x)=ln(sqrt(x^2-2x))

inverse

f (x) = ln (x^{2} - 2 x)

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

Solution steps

y = ln (x^{2} - 2 x)

Replace

x

with

y

x = ln (y^{2} - 2 y)

Solve for

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

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

12 - 2 x + \frac{5}{2}

f (x) = 1.5226 x

y = 2 π r^{2} + 2 π r h

2 π r

\frac{1}{1 - x ^{2}}

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