What is the inverse of e^x-e^{-x} ?

The inverse of e^x-e^{-x} is ln((x+sqrt(x^2+4))/2),ln((x-sqrt(x^2+4))/2)

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inverse of e^x-e^{-x}

inverse

e^{x} - e^{- x}

ln (\frac{x + x ^{2} + 4}{2}), ln (\frac{x - x ^{2} + 4}{2})

Solution steps

y = e^{x} - e^{- x}

Replace

x

with

y

x = e^{y} - e^{- y}

Solve for

y, x = e^{y} - e^{- y}

ln (\frac{x + x ^{2} + 4}{2}), ln (\frac{x - x ^{2} + 4}{2})

f (x) = \frac{1}{x + 4} + 3

f (x) = \frac{2 x - 5}{x + 3}

x

f (x) = 6 x - 24

f (x) = 0

What is the inverse of e^x-e^{-x} ?
The inverse of e^x-e^{-x} is ln((x+sqrt(x^2+4))/2),ln((x-sqrt(x^2+4))/2)