Question

How do you find the domain and range of `1/(x+2)`?

Answer 1

Domain: `(-oo,-2)uu(-2,+oo)`
Range: `(-oo,0) uu (0,+oo)`

Explanation:

`f(x) = 1/(x+2`

`f(x)` is defined `forall x in RR` except `x=-2`

Hence, the domain of `f(x)` in interval notation is`(-oo, -2)uu(-2, +oo)`

Consider `lim_(x->-2-) = -oo`

And `lim_(x->-2+) = +oo`

Also, `f(x) != 0` for any finite `x`

Hence, the range of `f(x)` is `(-oo,0) uu (0,+oo)`

As can be seen by the graph of `f(x)` below.

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