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

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

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

inverse

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

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

Solution steps

y = \frac{e ^{x} + e ^{- x}}{2}

Replace

x

with

y

x = \frac{e ^{y} + e ^{- y}}{2}

Solve for

y, x = \frac{e ^{y} + e ^{- y}}{2}

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

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