What is the inverse of f(x)=e^{(x+2)/(x-2)} ?

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

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inverse of f(x)=e^{(x+2)/(x-2)}

inverse

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

\frac{2 + 2 ln ( x )}{ln ( x ) - 1}

Solution steps

y = e^{\frac{x + 2}{x - 2}}

Replace

x

with

y

x = e^{\frac{y + 2}{y - 2}}

Solve for

y, x = e^{\frac{y + 2}{y - 2}}

\frac{2 + 2 ln ( x )}{ln ( x ) - 1}

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