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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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