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

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

inverse

f (x) = - 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})

\frac{- 3 x}{2 x + 5}

\frac{1}{2} x - 30

f (y) = 7 x - 2 y = 25

(33, 75), (3, - 5)

y = 2 x + 2

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