# How do you find the domain and range of #(x-1) / (x-2)#?

##### 1 Answer

The domain is

The range is

#### Explanation:

#f(x) = (x-1)/(x-2) = (x-2+1)/(x-2) = 1 + 1/(x-2)#

When

If we let

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

So:

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

So:

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

So:

#f^(-1)(y) = 2 + 1/(y-1)#

This is well defined for all

Since

To summarise:

The domain of

The range of

graph{(x-1)/(x-2) [-8.13, 11.87, -3.88, 6.12]}