Write the domain in interval notation. (a) \( k(x)=\frac{x+6}{x-2} \) (b) \( j(x)=\frac{x+6}{x^{2}+2} \) (c) \( p(x)=\frac{x+6}{x^{2}-2} \)

For the function \( k(x)=\frac{x+6}{x-2} \), the domain is all real numbers except where the denominator is zero. Thus, \( x-2 \neq 0 \) which gives us \( x \neq 2 \). In interval notation, the domain is \( (-\infty, 2) \cup (2, \infty) \). For the function \( j(x)=\frac{x+6}{x^{2}+2} \), the denominator \( x^2 + 2 \) is never zero for any real number, since \( x^2 \) is always non-negative and adding 2 keeps it positive. Therefore, the domain in interval notation is \( (-\infty, \infty) \). For the function \( p(x)=\frac{x+6}{x^{2}-2} \), the denominator needs to be considered, \( x^2 - 2 \neq 0 \). This gives us \( x^2 \neq 2 \) or \( x \neq \pm \sqrt{2} \). Thus, the domain in interval notation is \( (-\infty, -\sqrt{2}) \cup (-\sqrt{2}, \sqrt{2}) \cup (\sqrt{2}, \infty) \).