Question

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

Answer 1

See explanation.

Explanation:

The domain is the largest subset of `RR` for which the formula is defined. Here the only values excluded from the domain are the solutions of

`x^2-1=0`

`x^2-1=0 => x^2=1 => x=-1 vv x=1`

So the domain is: `D = RR-{-1;1}`

If we look at the graph:

graph{x/(x^2-1) [-10, 10, -5, 5]}

we can see that the range is `RR`

Solution:

Domain: `RR-{-1;1}`

Range: `RR`