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

Jan 20, 2018

See explanation.

#### Explanation:

The domain is the largest subset of $\mathbb{R}$ for which the formula is defined. Here the only values excluded from the domain are the solutions of

## ${x}^{2} - 1 = 0$

${x}^{2} - 1 = 0 \implies {x}^{2} = 1 \implies x = - 1 \vee x = 1$

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 $\mathbb{R}$

Solution: