What is the inverse of f(x)=ln(2x-1)-ln(3x+1)+2 ?

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

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inverse of f(x)=ln(2x-1)-ln(3x+1)+2

inverse

f (x) = ln (2 x - 1) - ln (3 x + 1) + 2

\frac{- e ^{2} - e ^{x}}{3 e ^{x} - 2 e ^{2}}

Solution steps

y = ln (2 x - 1) - ln (3 x + 1) + 2

Replace

x

with

y

x = ln (2 y - 1) - ln (3 y + 1) + 2

Solve for

y, x = ln (2 y - 1) - ln (3 y + 1) + 2

\frac{- e ^{2} - e ^{x}}{3 e ^{x} - 2 e ^{2}}

f (x) = \frac{x ^{2} - 9}{6 x ^{2}}

f (x) = arccos (\frac{5 x}{x + 12})

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

1 - 2 2 x - 5

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