Question

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

Answer 1

First note that for all `x in RR`, `x^2+7 >= 7`, so the denominator will always be non-zero.

Next note that `sqrt(x+7)` is defined when `x+7 >= 0`, that is when `x >= -7`.

So `f(x)` is well defined for `x in [-7, oo)` which is therefore the domain of `f(x)`.