Question

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

Answer 1

The domain is `x in (-oo,1) uu(1,+oo)`. The range is `y in (-oo,0)uu(0,+oo)`.

Explanation:

The function is

`f(x)=2/(x-1)`

As we cannot divide by `0`, the denominator must be `!=0`

`x-1!=0`

`x!=1`

The domain is `x in (-oo,1) uu(1,+oo)`

To find the range, let

`y=2/(x-1)`

`y(x-1)=2`

`yx-y=2`

`yx=2+y`

`x=(2+y)/y`

As we cannot divide by `0`, the denominator must be `!=0`

`y!=0`

The range is `y in (-oo,0)uu(0,+oo)`

graph{2/(x-1) [-12.66, 12.65, -6.33, 6.33]}