What is the inverse of f(x)=e^{(x-3)/(x+2)} ?

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

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inverse of f(x)=e^{(x-3)/(x+2)}

inverse

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

\frac{- 3 - 2 ln ( x )}{ln ( x ) - 1}

Solution steps

y = e^{\frac{x - 3}{x + 2}}

Replace

x

with

y

x = e^{\frac{y - 3}{y + 2}}

Solve for

y, x = e^{\frac{y - 3}{y + 2}}

\frac{- 3 - 2 ln ( x )}{ln ( x ) - 1}

4 x^{4}

2 + x - 1

f (x) = 10 (x + 8)^{7} - 10

f (x) = 2^{2 x - 1}

f (x) = - 2 + ln (x)

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