Originally Posted by

**ThePerfectHacker** The domain of $\displaystyle f\cdot g$ is the intersection of the domain of $\displaystyle f$ and $\displaystyle g$ which is still $\displaystyle \mathbb{R}$

The domain of $\displaystyle f/g$ is the intersection of the domain of $\displaystyle f$ and $\displaystyle g$ and $\displaystyle g\not = 0$ thus it is $\displaystyle \mathbb{R} \setminus \{ 0 \}$

$\displaystyle f\cdot g = \{ (x,y)|x\in \mathbb{R}, y = x(x^2-7x)\}$

$\displaystyle f/g = \{(x,y)| x\in \mathbb{R} \setminus \{ 0 \}, y = (x^2-7x)/x=x-7\}$