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

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Answer 1 · 2016-06-04T22:39:21

You can consider your $f^(-1)(x)$ as a new variable $y$ .
Then you write

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

now, to invert it, you want to obtain $x$ as function of $y$ .

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

$y+2=-1/(x-1)$

$-(y+2)=1/(x-1)$

$-1/(y+2)=x-1$

$1-1/(y+2)=x$

This is your inverse function.

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