Question

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

Answer 1

Domain: all Real values excluding `1`
Range: all Real values excluding `0`

Explanation:

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

Since division by `0` is undefined
`color(white)("XXX")x-1 != 0`
`color(white)("XXX")rarr x != 1`
However `f(x)` is defined for all other values of `x`

Since `f(x)=1/(x-1)`
then
`color(white)("XXX")(x-1)*f(x)=1`
and the question of "Range" becomes
`color(white)("XXX")`for what value(s) of `f(x)` is this not possible.
The only answer is that it is not possible if `f(x)=0`.
So the Range is all Real values except `0`