What is the inverse of f(x)=(e^x)/(7+2e^x) ?

The inverse of f(x)=(e^x)/(7+2e^x) is ln(-(7x)/(2x-1))

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inverse of f(x)=(e^x)/(7+2e^x)

inverse

f (x) = \frac{e ^{x}}{7 + 2 e ^{x}}

ln (- \frac{7 x}{2 x - 1})

Solution steps

y = \frac{e ^{x}}{7 + 2 e ^{x}}

Replace

x

with

y

x = \frac{e ^{y}}{7 + 2 e ^{y}}

Solve for

y, x = \frac{e ^{y}}{7 + 2 e ^{y}}

ln (- \frac{7 x}{2 x - 1})

What is the inverse of f(x)=(e^x)/(7+2e^x) ?
The inverse of f(x)=(e^x)/(7+2e^x) is ln(-(7x)/(2x-1))