The functions $$ f $$ and $$ g $$ are defined as follows. $$ f(x)=\frac{x^{2}}{x+8} $$ $$ g(x)=\frac{x+6}{x^{2}-36} $$ For each function, find the domain. Write each answer as an interval or union of intervals. Domain of $$ f: $$ Domain of $$ g: \square $$

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1. **Domain of $$ f(x)=\frac{x^2}{x+8} $$:**

- The function $$ f(x) $$ is undefined when its denominator equals zero.
   - Set the denominator equal to zero:
     $$
     x+8=0 \quad \Rightarrow \quad x=-8.
     $$
   - Therefore, $$ x=-8 $$ must be excluded from the domain.
   - The domain of $$ f $$ in interval notation is:
     $$
     (-\infty,-8)\cup(-8,\infty).
     $$

2. **Domain of $$ g(x)=\frac{x+6}{x^2-36} $$:**

- The function $$ g(x) $$ is undefined when its denominator equals zero.
   - Factor the denominator:
     $$
     x^2-36=(x-6)(x+6).
     $$
   - Set each factor equal to zero:
     $$
     x-6=0 \quad \Rightarrow \quad x=6,
     $$
     $$
     x+6=0 \quad \Rightarrow \quad x=-6.
     $$
   - Even though the numerator $$ x+6 $$ is the same as one of the factors, cancellation (if performed) would define a removable discontinuity, but the original function is still undefined at $$ x=-6 $$.
   - Thus, both $$ x=-6 $$ and $$ x=6 $$ must be excluded.
   - The domain of $$ g $$ in interval notation is:
     $$
     (-\infty,-6)\cup(-6,6)\cup(6,\infty).
     $$

**Final Answers:**

Domain of $$ f: (-\infty,-8)\cup(-8,\infty) $$

Domain of $$ g: (-\infty,-6)\cup(-6,6)\cup(6,\infty) $$
Domain of $$ f: (-\infty,-8) \cup (-8,\infty) $$ Domain of $$ g: (-\infty,-6) \cup (-6,6) \cup (6,\infty) $$

The functions \( f \) and \( g \) are defined as follows. \[ f(x)=\frac{x^{2}}{x+8} \] \( g(x)=\frac{x+6}{x^{2}-36} \) For each function, find the domain. Write each answer as an interval or union of intervals. Domain of \( f: \) Domain of \( g: \square \)

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