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

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

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inverse of f(x)= 1/(e^{-x)}+1/(e^{-2x)}

inverse

f (x) = \frac{1}{e ^{- x}} + \frac{1}{e ^{- 2 x}}

ln (\frac{- 1 + 1 + 4 x}{2}), ln (\frac{- 1 - 1 + 4 x}{2})

Solution steps

y = \frac{1}{e ^{- x}} + \frac{1}{e ^{- 2 x}}

Replace

x

with

y

x = \frac{1}{e ^{- y}} + \frac{1}{e ^{- 2 y}}

Solve for

y, x = \frac{1}{e ^{- y}} + \frac{1}{e ^{- 2 y}}

ln (\frac{- 1 + 1 + 4 x}{2}), ln (\frac{- 1 - 1 + 4 x}{2})

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