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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

ln (5 x + 1) - 7

f (x) = x - 3 + 1

f (x) = \frac{d - 12}{2 d + 1}

f (x) = \frac{2 x + 5}{7 x + 6}

f (x) = \frac{5 x - 1}{- x + 2}

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