What is the inverse of f(x)= 4/(1+ln(1+e^x)) ?

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

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inverse of f(x)= 4/(1+ln(1+e^x))

inverse

f (x) = \frac{4}{1 + ln ( 1 + e ^{x} )}

ln (e^{\frac{4}{x} - 1} - 1)

Solution steps

y = \frac{4}{1 + ln ( 1 + e ^{x} )}

Replace

x

with

y

x = \frac{4}{1 + ln ( 1 + e ^{y} )}

Solve for

y, x = \frac{4}{1 + ln ( 1 + e ^{y} )}

ln (e^{\frac{4}{x} - 1} - 1)

f (x) = 3 x^{3} + 9

f (x) = 3 x^{3} + 3

f (x) = \frac{3 x}{5 x - 8}

f (x) = \frac{x}{3} + \frac{2}{3}

f (x) = x - 1 - 3

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