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

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

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inverse of f(x)=(e^{4x})/(3+e^{4x)}

inverse

f (x) = \frac{e ^{4 x}}{3 + e ^{4 x}}

\frac{ln ( - \frac{3 x}{x - 1} )}{4}

Solution steps

y = \frac{e ^{4 x}}{3 + e ^{4 x}}

Replace

x

with

y

x = \frac{e ^{4 y}}{3 + e ^{4 y}}

Solve for

y, x = \frac{e ^{4 y}}{3 + e ^{4 y}}

\frac{ln ( - \frac{3 x}{x - 1} )}{4}

7 x - 8 y = 0

x^{4} - x^{2}

f (x) = \frac{7}{x - 4}

y = 11 x - 5

(x^{2} - 9)^{6}

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