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

The inverse of 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 1/2*(e^x+e^{-x})

inverse

\frac{1}{2} \cdot (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} \cdot (e^{y} + e^{- y})

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

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