What is the inverse of f(x)=(5^x)/(1+5^x) ?

The inverse of f(x)=(5^x)/(1+5^x) is (ln(-x/(x-1)))/(ln(5))

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inverse of f(x)=(5^x)/(1+5^x)

inverse

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

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

Solution steps

y = \frac{5 ^{x}}{1 + 5 ^{x}}

Replace

x

with

y

x = \frac{5 ^{y}}{1 + 5 ^{y}}

Solve for

y, x = \frac{5 ^{y}}{1 + 5 ^{y}}

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

\frac{2 x + 3}{x - 4}

f (x) = x - 3 - 4

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

y = 8^{x}

f (x) = \frac{2}{5} x - 3

What is the inverse of f(x)=(5^x)/(1+5^x) ?
The inverse of f(x)=(5^x)/(1+5^x) is (ln(-x/(x-1)))/(ln(5))