What is the inverse of f(x)=(3^x)/(3+3^x) ?

The inverse of f(x)=(3^x)/(3+3^x) is (ln(-\frac{3x)/(x-1))}{ln(3)}

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inverse of f(x)=(3^x)/(3+3^x)

inverse

f (x) = \frac{3 ^{x}}{3 + 3 ^{x}}

\frac{ln ( - \frac{3 x}{x - 1} )}{ln ( 3 )}

Solution steps

y = \frac{3 ^{x}}{3 + 3 ^{x}}

Replace

x

with

y

x = \frac{3 ^{y}}{3 + 3 ^{y}}

Solve for

y, x = \frac{3 ^{y}}{3 + 3 ^{y}}

\frac{ln ( - \frac{3 x}{x - 1} )}{ln ( 3 )}

\frac{2}{x ^{2} - 2 x - 3}

f (x) = \frac{2 x - 4}{x - 3}

\frac{2 ^{4 x - 1} \cdot 3 ^{x - 2}}{1 2 ^{x - 2}}

\frac{6 x - 2}{2 x + 6}

\frac{23 - 3 x}{6 x}

What is the inverse of f(x)=(3^x)/(3+3^x) ?
The inverse of f(x)=(3^x)/(3+3^x) is (ln(-\frac{3x)/(x-1))}{ln(3)}