What is the inverse of f(x)=((e^x-3))/((2e^x+1)) ?

The inverse of f(x)=((e^x-3))/((2e^x+1)) is ln((-3-x)/(2x-1))

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inverse of f(x)=((e^x-3))/((2e^x+1))

inverse

f (x) = \frac{( e ^{x} - 3 )}{( 2 e ^{x} + 1 )}

ln (\frac{- 3 - x}{2 x - 1})

Solution steps

y = \frac{e ^{x} - 3}{2 e ^{x} + 1}

Replace

x

with

y

x = \frac{e ^{y} - 3}{2 e ^{y} + 1}

Solve for

y, x = \frac{e ^{y} - 3}{2 e ^{y} + 1}

ln (\frac{- 3 - x}{2 x - 1})

f (x) = \frac{4 - 3 x}{7 - 9 x}

f (x) = (x^{\frac{1}{5}} - 7)^{7}

f (x) = \frac{x}{2 x - 6}

g (x) = lo g_{3} (x)

f (x) = x - 4 + 2

What is the inverse of f(x)=((e^x-3))/((2e^x+1)) ?
The inverse of f(x)=((e^x-3))/((2e^x+1)) is ln((-3-x)/(2x-1))