What is the inverse of f(x)=ln(x+sqrt(x^2+1)) ?

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

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inverse of f(x)=ln(x+sqrt(x^2+1))

inverse

f (x) = ln (x + x^{2} + 1)

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

Solution steps

y = ln (x + x^{2} + 1)

Replace

x

with

y

x = ln (y + y^{2} + 1)

Solve for

y, x = ln (y + y^{2} + 1)

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

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