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

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Answer 1 · 2015-04-08T15:39:43

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]}

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