What is the inverse of f(x)=ln((5-x)/(x+2)) ?

The inverse of f(x)=ln((5-x)/(x+2)) is (5-2e^x)/(e^x+1)

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inverse of f(x)=ln((5-x)/(x+2))

inverse

f (x) = ln (\frac{5 - x}{x + 2})

\frac{5 - 2 e ^{x}}{e ^{x} + 1}

Solution steps

y = ln (\frac{5 - x}{x + 2})

Replace

x

with

y

x = ln (\frac{5 - y}{y + 2})

Solve for

y, x = ln (\frac{5 - y}{y + 2})

\frac{5 - 2 e ^{x}}{e ^{x} + 1}

What is the inverse of f(x)=ln((5-x)/(x+2)) ?
The inverse of f(x)=ln((5-x)/(x+2)) is (5-2e^x)/(e^x+1)