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

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

inverse

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

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

Solution steps

y = \frac{1}{e ^{- x}} + \frac{1}{e ^{x}}

Replace

x

with

y

x = \frac{1}{e ^{- y}} + \frac{1}{e ^{y}}

Solve for

y, x = \frac{1}{e ^{- y}} + \frac{1}{e ^{y}}

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

What is the inverse of f(x)= 1/(e^{-x)}+1/(e^x) ?
The inverse of f(x)= 1/(e^{-x)}+1/(e^x) is ln((x+sqrt(x^2-4))/2),ln((x-sqrt(x^2-4))/2)