What is the inverse of f(x)=((6e^x-4)/(8e^x+6)) ?

The inverse of f(x)=((6e^x-4)/(8e^x+6)) is ln(-(3x+2)/(4x-3))

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inverse of f(x)=((6e^x-4)/(8e^x+6))

inverse

f (x) = (\frac{6 e ^{x} - 4}{8 e ^{x} + 6})

ln (- \frac{3 x + 2}{4 x - 3})

Solution steps

y = \frac{6 e ^{x} - 4}{8 e ^{x} + 6}

Replace

x

with

y

x = \frac{6 e ^{y} - 4}{8 e ^{y} + 6}

Solve for

y, x = \frac{6 e ^{y} - 4}{8 e ^{y} + 6}

ln (- \frac{3 x + 2}{4 x - 3})

f (x) = \frac{- 5 x - 20}{7}

f (x) = \frac{2 x}{12} + \frac{5}{12}

- (x + 1)^{2} - 2, (x \leq 1)

sin (0.9622)

\frac{3}{- x - 1} + 1

What is the inverse of f(x)=((6e^x-4)/(8e^x+6)) ?
The inverse of f(x)=((6e^x-4)/(8e^x+6)) is ln(-(3x+2)/(4x-3))