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

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

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

inverse

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

\frac{- 3 - 2 e ^{x}}{e ^{x} - 1}

Solution steps

y = ln (\frac{x - 3}{x + 2})

Replace

x

with

y

x = ln (\frac{y - 3}{y + 2})

Solve for

y, x = ln (\frac{y - 3}{y + 2})

\frac{- 3 - 2 e ^{x}}{e ^{x} - 1}

(0, 0), (- 3, 5)

f (x) = 3 (3 x + 4)

f (x) = 3 x^{2} - 12

sin^{4} (x)

f (x) = \frac{8 + x}{3 x - 2}

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