What is the inverse of f(x)=32-20e^{-0.4x} ?

The inverse of f(x)=32-20e^{-0.4x} is -(ln(-\frac{x-32)/(20))}{0.4}

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inverse of f(x)=32-20e^{-0.4x}

inverse

f (x) = 32 - 20 e^{- 0.4 x}

- \frac{ln ( - \frac{x - 32}{20} )}{0.4}

Solution steps

y = 32 - 20 e^{- 0.4 x}

Replace

x

with

y

x = 32 - 20 e^{- 0.4 y}

Solve for

y, x = 32 - 20 e^{- 0.4 y}

- \frac{ln ( - \frac{x - 32}{20} )}{0.4}

What is the inverse of f(x)=32-20e^{-0.4x} ?
The inverse of f(x)=32-20e^{-0.4x} is -(ln(-\frac{x-32)/(20))}{0.4}