How do you find the inverse of $f(x)=In(3-2x)+3$ ?

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Answer 1 · 2016-03-11T04:47:05

x = $( 3-e^(y-3))/2$ , where y = f(x).

Using y = f (x ),

$e^(y-3)=e^(ln(3-2x))$

= $(3-2x)$
Rearrange for the inverse relation

$x = ( 3-e^(y-3))/2$

The graphs for both are one and the same.

Observe that x < 1.5.
graph{y - ln ( 3 - 2x )-3=0}

graph{x-1.5+0.5(2.718)^(y-3)=0}

Important for inverters:

For inverse of $y == abs f(x)$ , use my explanation for the inverse

operator $(abs)^(-1)$ .

$x = (abs)^(-1) (y)$ , where

$(abs)^(-1) (y) = y, f(x) >= 0$ and

$(abs)^(-1) (y) = -y, f(x) <= 0$ .

For example, if $y = abs(x-1)$ ,

$x - 1 = (abs)^(-1)(y)$

$= y, x - 1 >= 0$ and

$= -y, x - 1 <= 0$ .

How do you find the inverse of f(x)=In(3-2x)+3f(x)=In(3-2x)+3?