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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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