How do you find the inverse of $f(x)= 1- ln(x-2)$ ?

Question

5666 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-11T05:08:44

The inverse of $f(x)$ is $e^(1-x)+2$

First, we take our function $f(x)=y$ :

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

Then switch the variables:

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

Solve for $y$ .

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

Remember that for any $e^x=b,$ we take that $lnb=x$ . Here:

$y-2=e^(1-x)$

$y=e^(1-x)+2$

The inverse of $f(x)$ is $e^(1-x)+2$

How do you find the inverse of f(x)= 1- ln(x-2)f(x)= 1- ln(x-2)?