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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = x^{2} + 6 x + 5

f (x) = x^{3} - 4 x^{2} + 4 x

f (x) = 9 x - 9

(x^{2} - 1) e^{- 2 x}

f (x) = 3 + 4 x^{2} - \frac{1}{2} x^{4}

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