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

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Answer 1 · 2015-11-22T22:04:02

Inverse is $f^-1(x) = 3/2 - (e^(x-3))/2$

Make $x$ the subject in this equation $y= ln(3-2x) + 3$

Step 1) $y-3 = ln(3-2x)$

Step 2) Make exponential expression on both sides to get rid of $ln$ so $e^(y-3) = 3-2x$

Step 3) The final form $x= 3/2 - (e^(y-3))/2$

Step 4) Final step replace x by $f^-1 (x)$ and $y$ by $x$ .

Hope that helps,
Cheers.

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