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

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

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

inverse

\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})

7 x + 1

y = \frac{x - 1}{x + 1}

y = 5 (0. 5^{- x})

f (x) = ln (4 x + 1)

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

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