The function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x)=\frac{x}{x^2+1} \quad \forall x \in \mathbb{R}$ is

A function $f$ from the set of natural numbers to integers defined by

$$f(n)=\left\{\begin{array}{l} \frac{n-1}{2}, \quad \text { when } n \text { is odd } \\ -\frac{n}{2}, \quad \text { when } n \text { is even } \end{array} \quad\right. \text { is }$$

The domain of the function $$y=\frac{1}{\log _{10}(3-x)}+\sqrt{x+7}$$ is