Find the domain of f /g (x).

Question

f(x) = x² + x,    g(x) = x²

Answer 1

The domain of f is all reals.

The domain of g is all reals.

The domain of f/g, therefore is all reals EXCEPT where g(x) = 0, which is at x = 0.

Therefore, the domain of f/g is

x ≠ 0

or

x < 0 or x > 0 - with inequalities

or

(-∞, 0) ∪ (0, ∞) - interval notation