What is the inverse of f(x)=(ln(x/(3-x)))/4 ?

The inverse of f(x)=(ln(x/(3-x)))/4 is (3e^{4x})/(1+e^{4x)}

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inverse of f(x)=(ln(x/(3-x)))/4

inverse

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

\frac{3 e ^{4 x}}{1 + e ^{4 x}}

Solution steps

y = \frac{ln ( \frac{x}{3 - x} )}{4}

Replace

x

with

y

x = \frac{ln ( \frac{y}{3 - y} )}{4}

Solve for

y, x = \frac{ln ( \frac{y}{3 - y} )}{4}

\frac{3 e ^{4 x}}{1 + e ^{4 x}}

What is the inverse of f(x)=(ln(x/(3-x)))/4 ?
The inverse of f(x)=(ln(x/(3-x)))/4 is (3e^{4x})/(1+e^{4x)}