The functions $$ f $$ and $$ g $$ are defined as follows. $$ f(x)=\frac{x^{2}}{x+4} $$ $$ g(x)=\frac{x-8}{x^{2}-64} $$ For each function, find the domain. Write each answer as an interval or union of intervals. Domain of $$ f $$ :

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Domain of $$ f $$: $$ (-\infty, -4) \cup (-4, \infty) $$ To find the domain of the function $$ f(x) = \frac{x^2}{x + 4} $$, we need to determine the values of $$ x $$ for which the function is defined. The function is a rational function, and it is defined as long as the denominator is not equal to zero. 1. Identify the denominator: $$ x + 4 $$ 2. Set the denominator equal to zero and solve for $$ x $$: $$ x + 4 = 0 \implies x = -4 $$ 3. The function $$ f(x) $$ is undefined at $$ x = -4 $$. Therefore, the domain of $$ f $$ includes all real numbers except $$ -4 $$. 4. In interval notation, the domain of $$ f $$ is: $$ (-\infty, -4) \cup (-4, \infty) $$ Thus, the domain of $$ f $$ is: $$ \boxed{(-\infty, -4) \cup (-4, \infty)} $$

The functions \( f \) and \( g \) are defined as follows. \[ f(x)=\frac{x^{2}}{x+4} \] \( g(x)=\frac{x-8}{x^{2}-64} \) For each function, find the domain. Write each answer as an interval or union of intervals. Domain of \( f \) :

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The functions \( f \) and \( g \) are defined as follows. \[ f(x)=\frac{x^{2}}{x+4} \] \( g(x)=\frac{x-8}{x^{2}-64} \) For each function, find the domain. Write each answer as an interval or union of intervals. Domain of \( f \) :

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