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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

\frac{- x ^{2} + 1}{( x ^{2} + 1 ) ^{2}}

f (x) = \frac{x - 5}{x + 1}

- 0.1 x^{2} + 0.7 x + 6

38 (e^{t} - 1)

f (x) = (\frac{( 2 x - 1 )}{( x - 3 )})

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