What is the inverse of f(x)=(2^x)/(5+2^x) ?

The inverse of f(x)=(2^x)/(5+2^x) is (ln(-\frac{5x)/(x-1))}{ln(2)}

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inverse of f(x)=(2^x)/(5+2^x)

inverse

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

\frac{ln ( - \frac{5 x}{x - 1} )}{ln ( 2 )}

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = \frac{2 ^{y}}{5 + 2 ^{y}}

\frac{ln ( - \frac{5 x}{x - 1} )}{ln ( 2 )}

y = - (x + 3)^{2}

f (x) = 3 + 3 x - 2

y = 50 - \frac{2}{3} x

f (r) = 2 π r^{2} + 16 π r

f (x) = 4 cos (1 - 2 x) + \frac{π}{3}

What is the inverse of f(x)=(2^x)/(5+2^x) ?
The inverse of f(x)=(2^x)/(5+2^x) is (ln(-\frac{5x)/(x-1))}{ln(2)}