Question

How do you find the domain for `h(x)=(x+2)/sqrt(x^2 - 7)`?

Answer 1

Anything that makes the denominator `=0` is forbidden.
Also, because of the root, `x^2-7` must be non-negative.

Together: `x^2-7>0->x^2>7`

This means that either `x>sqrt7` or `x<-sqrt7`

See graph (`sqrt7~~2.65`)
graph{(x+2)/sqrt(x^2-7) [-10, 10, -5, 5]}