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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = 1 - x + 1

g (x) = 1 - 3 x

f (x) = x - 4 + 10

f (x) = 3 + x + 2

g (x) = 3 x + 1

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