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}

y = (x + 1)^{2}

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

f (x) = x^{2} + y^{2} x^{2} - 4 y^{2} = 0

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

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)