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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

(- 3, 1), (- 3, 5)

f (x) = - x^{3} + 12 x - 10

(1, 2), (5, 5)

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

2^{x} + 3

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