# How do you find the domain in interval notation for f(x)=sqrt(x+7)/(x^2+7)?

First note that for all $x \in \mathbb{R}$, ${x}^{2} + 7 \ge 7$, so the denominator will always be non-zero.
Next note that $\sqrt{x + 7}$ is defined when $x + 7 \ge 0$, that is when $x \ge - 7$.
So $f \left(x\right)$ is well defined for $x \in \left[- 7 , \infty\right)$ which is therefore the domain of $f \left(x\right)$.