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

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

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inverse of f(x)=(1-ln(2x))/(2+3ln(2x))

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = \frac{1 - ln ( 2 y )}{2 + 3 ln ( 2 y )}

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

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

f (x) = \frac{20 - x}{4}

f (x) = \frac{x}{2 x - 9}

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

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