What is the inverse of f(x)=ln(x/(2x-1)) ?

The inverse of f(x)=ln(x/(2x-1)) is (e^x)/(2e^x-1)

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inverse of f(x)=ln(x/(2x-1))

inverse

f (x) = ln (\frac{x}{2 x - 1})

\frac{e ^{x}}{2 e ^{x} - 1}

Solution steps

y = ln (\frac{x}{2 x - 1})

Replace

x

with

y

x = ln (\frac{y}{2 y - 1})

Solve for

y, x = ln (\frac{y}{2 y - 1})

\frac{e ^{x}}{2 e ^{x} - 1}

x + 2 - 2 x + 3

f (x) = 2^{x - 3} - 5, (4, 7)

f (x) = ((3 \cdot x - 1))

f (x) = \frac{5 x + 7}{3 x - 5}

2^{x^{2} + 2 x}

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