What is the inverse of f(x)=(2e^x-7)/(18e^x+12) ?

The inverse of f(x)=(2e^x-7)/(18e^x+12) is ln((-7-12x)/(2(-1+9x)))

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inverse of f(x)=(2e^x-7)/(18e^x+12)

inverse

f (x) = \frac{2 e ^{x} - 7}{18 e ^{x} + 12}

ln (\frac{- 7 - 12 x}{2 ( - 1 + 9 x )})

Solution steps

y = \frac{2 e ^{x} - 7}{18 e ^{x} + 12}

Replace

x

with

y

x = \frac{2 e ^{y} - 7}{18 e ^{y} + 12}

Solve for

y, x = \frac{2 e ^{y} - 7}{18 e ^{y} + 12}

ln (\frac{- 7 - 12 x}{2 ( - 1 + 9 x )})

- x^{2} + 6 x + 2

\frac{12}{x}

4 x + 6 y = 1

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

(- 4, 3), (4, - 1)

What is the inverse of f(x)=(2e^x-7)/(18e^x+12) ?
The inverse of f(x)=(2e^x-7)/(18e^x+12) is ln((-7-12x)/(2(-1+9x)))