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**Greengoblin** hi, thanks, when you say 'does not hit all the points in the domain' do you mean for example that there are some values belonging to the domain, for which the function does not have a value? So for example $\displaystyle f:\mathbb{R}\rightarrow\mathbb{R}$ where $\displaystyle f(x)=+\sqrt{x}$ is not actually a well defined function since for negative $\displaystyle \{x\in\mathbb{R}:x<0\}$ (in the domain), the function doesn't make sense? Meaning we need to restrict the domain.