What is the inverse of f(x)=1-e^{-0.5x} ?

The inverse of f(x)=1-e^{-0.5x} is -(ln(1-x))/(0.5)

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inverse of f(x)=1-e^{-0.5x}

inverse

f (x) = 1 - e^{- 0.5 x}

- \frac{ln ( 1 - x )}{0.5}

Solution steps

y = 1 - e^{- 0.5 x}

Replace

x

with

y

x = 1 - e^{- 0.5 y}

Solve for

y, x = 1 - e^{- 0.5 y}

- \frac{ln ( 1 - x )}{0.5}

f (x) = t^{2} - 9

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

y = - 2 x + 2

\frac{x ^{2} - 9}{x ^{2} + 1}

y = 2 - x

What is the inverse of f(x)=1-e^{-0.5x} ?
The inverse of f(x)=1-e^{-0.5x} is -(ln(1-x))/(0.5)