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

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

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inverse of f(x)=(2e^x+3)/(e^x-4)

inverse

f (x) = \frac{2 e ^{x} + 3}{e ^{x} - 4}

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

Solution steps

y = \frac{2 e ^{x} + 3}{e ^{x} - 4}

Replace

x

with

y

x = \frac{2 e ^{y} + 3}{e ^{y} - 4}

Solve for

y, x = \frac{2 e ^{y} + 3}{e ^{y} - 4}

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

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