Question

How do you find the domain in interval notation for `f(x)=x/(x^3+8)`?

Answer 1

`(x^3 + 8) = (x^3+2^3) = (x+2)(x^2-2x+4)`

has only one zero for real values of `x`, viz `x = -2`.

`f(x)` is well defined for all other values of `x`.

So the domain of `f(x)` is `(-oo, -2) uu (-2, oo)`