What is the inverse of f(x)=ln(x/(4x-3)) ?

The inverse of f(x)=ln(x/(4x-3)) is (3e^x)/(4e^x-1)

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inverse of f(x)=ln(x/(4x-3))

inverse

f (x) = ln (\frac{x}{4 x - 3})

\frac{3 e ^{x}}{4 e ^{x} - 1}

Solution steps

y = ln (\frac{x}{4 x - 3})

Replace

x

with

y

x = ln (\frac{y}{4 y - 3})

Solve for

y, x = ln (\frac{y}{4 y - 3})

\frac{3 e ^{x}}{4 e ^{x} - 1}

\frac{4 x}{5 x - 6}

f (x) = \frac{x}{4} + \frac{1}{4}

sin (0.6899)

f (x) = f (x) = x^{2}

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

What is the inverse of f(x)=ln(x/(4x-3)) ?
The inverse of f(x)=ln(x/(4x-3)) is (3e^x)/(4e^x-1)