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

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

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

inverse

f (x) = \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 )}

5 lo g_{e} (x - 10)

f (x) = \frac{8 x}{x - 2}

f (x) = \frac{5 x + 25}{9}

y = 2 π r^{2} + 8 π r

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

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