What is the inverse of f(x)=(5e^x-8)/(e^x+10) ?

The inverse of f(x)=(5e^x-8)/(e^x+10) is ln((-8-10x)/(x-5))

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inverse of f(x)=(5e^x-8)/(e^x+10)

inverse

ln (\frac{- 8 - 10 x}{x - 5})

Solution steps

y = \frac{5 e ^{x} - 8}{e ^{x} + 10}

Replace

x

with

y

x = \frac{5 e ^{y} - 8}{e ^{y} + 10}

Solve for

y, x = \frac{5 e ^{y} - 8}{e ^{y} + 10}

ln (\frac{- 8 - 10 x}{x - 5})

What is the inverse of f(x)=(5e^x-8)/(e^x+10) ?
The inverse of f(x)=(5e^x-8)/(e^x+10) is ln((-8-10x)/(x-5))