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

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

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

inverse

f (x) = ln (x - 1) - ln (2 x + 1)

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

Solution steps

y = ln (x - 1) - ln (2 x + 1)

Replace

x

with

y

x = ln (y - 1) - ln (2 y + 1)

Solve for

y, x = ln (y - 1) - ln (2 y + 1)

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

f (x) = lo g_{5} (2 x + 4)

f (x) = \frac{2 x - 7}{5 x + 1}

f (x) = 3 sin (x) + 2

7 + ln (3 x + 1)

f (x) = 100 - x^{2}

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