Question

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

Answer 1

Domain: `(-oo, 1) uu (1, +oo)`
Range: `(-oo, 0) uu (0, + oo)`

Explanation:

The domain of the function will be restricted by the fact that the denominator cannot be equal to zero.

`x-1!=0 implies x!=1`

The domain will thus be `RR-{1}`, or `(-oo, 1) uu (1, +oo)`.

The range of the function will be restricted by the fact that this expression cannot be equal to zero, since the numerator is a constant.

The range of the function will thus be `RR-{0}`, or `(-oo, 0) uu (0, + oo)`.

graph{2/(x-1) [-7.9, 7.9, -3.95, 3.95]}