What is the inverse of f(x)=((5e^x))/(-5e^x+1) ?

The inverse of f(x)=((5e^x))/(-5e^x+1) is ln(x/(5(x+1)))

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inverse of f(x)=((5e^x))/(-5e^x+1)

inverse

f (x) = \frac{( 5 e ^{x} )}{- 5 e ^{x} + 1}

ln (\frac{x}{5 ( x + 1 )})

Solution steps

y = \frac{5 e ^{x}}{- 5 e ^{x} + 1}

Replace

x

with

y

x = \frac{5 e ^{y}}{- 5 e ^{y} + 1}

Solve for

y, x = \frac{5 e ^{y}}{- 5 e ^{y} + 1}

ln (\frac{x}{5 ( x + 1 )})

y = \frac{10}{7} x - 3, (5, - 4)

f (x) = (\frac{x ^{3} + 2}{x ^{2} - 9})

f (x) = \frac{1}{x ^{3}}

\frac{1}{1 - \frac{1}{x - 2}}

x^{4} - 4 x^{2}

What is the inverse of f(x)=((5e^x))/(-5e^x+1) ?
The inverse of f(x)=((5e^x))/(-5e^x+1) is ln(x/(5(x+1)))