Question

What is the domain and range of `y=1/(x-1)^2`?

Answer 1

Domain: `x in RR`, `x ne 1`.
Range: `y>0`

Explanation:

The graph of `y=1/x^2` has domain `x in RR`, `x ne 0` and `y>0`.

`y=1/(x-1)^2` is a horizontal shift of 1 unit to the right, so the new domain is `x in RR`, `x ne 1`. The range does not change, so it's still `y>0`.