What is the inverse of y=(2^x)/(3+2^x) ?

The inverse of y=(2^x)/(3+2^x) is (ln(-\frac{3x)/(x-1))}{ln(2)}

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inverse of y=(2^x)/(3+2^x)

inverse

y = \frac{2 ^{x}}{3 + 2 ^{x}}

\frac{ln ( - \frac{3 x}{x - 1} )}{ln ( 2 )}

Solution steps

y = \frac{2 ^{x}}{3 + 2 ^{x}}

Replace

x

with

y

x = \frac{2 ^{y}}{3 + 2 ^{y}}

Solve for

y, x = \frac{2 ^{y}}{3 + 2 ^{y}}

\frac{ln ( - \frac{3 x}{x - 1} )}{ln ( 2 )}

2 arccos (\frac{x}{3})

f (x) = - 3 x^{2} + 1

2 \cdot ln (x^{3})

f (x) = x + 43 x - 2

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

What is the inverse of y=(2^x)/(3+2^x) ?
The inverse of y=(2^x)/(3+2^x) is (ln(-\frac{3x)/(x-1))}{ln(2)}