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

The inverse of f(x)=a(1-1/(1-2^{-x)}) is -(ln(-x/(-x+a)))/(ln(2))

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

inverse

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

- \frac{ln ( - \frac{x}{- x + a} )}{ln ( 2 )}

Solution steps

y = a (1 - \frac{1}{1 - 2 ^{- x}})

Replace

x

with

y

x = a (1 - \frac{1}{1 - 2 ^{- y}})

Solve for

y, x = a (1 - \frac{1}{1 - 2 ^{- y}})

- \frac{ln ( - \frac{x}{- x + a} )}{ln ( 2 )}

f (x) = - x^{3} + 9 x^{2} - 52

\frac{1}{x ^{2}}

f (x) = 5 x - 3

\frac{x ^{2} + 5}{2}

h (x) = \frac{5}{7} x^{5} - 3

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