Question

What is the domain of `F(x)= (x-2)/( x^3+x)`?

Answer 1

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

Explanation:

`F(x)= (x-2)/(x^3+x)`

`= (x-2)/(x(x^2+1))`

`F(x)` is defined for all `x` except where `x(x^2+1) =0`

Since `(x^2+1) >=1 forall x in RR`

`-> F(x)` is defined `forall x in RR: x!=0`

Hence the domain of `F(x)` is `(-oo,0)uu(0,+oo)`

As can be deduced from the graph of `F(x)` below.

graph{(x-2)/(x^3+x) [-10, 10, -5, 5]}