Domain

What is the domain?

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\( f(x) = \frac{x + 6}{\sqrt{x^2 - 4}}\)

\(\color{blue}\mathbb D=\mathbb R\ |\ x\in \{-2\leq x\leq 2\}\)

  !

Things inside any square root must be nonnegative and the denominator is nonzero.

\(x^2 - 4 \geq 0\text{ and } \sqrt{x^2 - 4} \neq 0 \\ x^2 - 4 \geq 0 \text{ and }x^2 - 4 \neq 0\\ x^2 - 4 > 0\)

Continue to solve the inequality, and you will get the domain of the function. 

\(\operatorname{Domain}(f) = \{x \in \mathbb R:-2 < x < 2\}\)