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

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

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inverse of f(x)= 1/2 (e^x-e^{-x})

inverse

f (x) = \frac{1}{2} (e^{x} - e^{- x})

ln (x + x^{2} + 1), ln (x - x^{2} + 1)

Solution steps

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

Replace

x

with

y

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

Solve for

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

ln (x + x^{2} + 1), ln (x - x^{2} + 1)

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