Determine the domain of the function. $$ f(x)=\frac{x^{2}}{8-x} $$

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1. Identify the function:  
   $$
   f(x)=\frac{x^{2}}{8-x}
   $$

2. The domain of the function consists of all $$ x $$ values for which the function is defined. For a rational function, the main restriction comes from the denominator: it cannot be equal to zero.

3. Set the denominator equal to zero and solve for $$ x $$:  
   $$
   8 - x = 0
   $$

4. Solve for $$ x $$:  
   $$
   x = 8
   $$

5. Since $$ x = 8 $$ makes the denominator zero, it must be excluded from the domain.

6. Therefore, the domain of $$ f(x) $$ is all real numbers except $$ x = 8 $$. In mathematical notation, the domain is:  
   $$
   \{x \in \mathbb{R} \mid x \neq 8\}
   $$
The domain of the function $$ f(x) = \frac{x^{2}}{8 - x} $$ is all real numbers except $$ x = 8 $$.

Determine the domain of the function. \( f(x)=\frac{x^{2}}{8-x} \)

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