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

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

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inverse of f(x)=(2^x)/(2^x+1)

inverse

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

\frac{ln ( - \frac{x}{x - 1} )}{ln ( 2 )}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{ln ( - \frac{x}{x - 1} )}{ln ( 2 )}

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