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})

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

f (x) = - 8 x + 8

f (x) = 4 x + 12

f (x) = \frac{8}{e ^{x - 3} + 6}

f (x) = 25 x - 18

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)