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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

1 + t^{2}

f (x) = 3 sin (π x)

y = 2 t + tan (t)

f (x) = \frac{x + 1}{5 x + 4}

y = \frac{x - 1}{x ^{2} - 9}

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