To find the domain of the rational function \( f(x) = \frac{2x}{x + 12} \), we need to identify any values of \( x \) that would make the denominator zero since division by zero is undefined.
The denominator is:
\[ x + 12 \]
Setting the denominator equal to zero to find the restricted values:
\[ x + 12 = 0 \]
Solving for \( x \):
\[ x = -12 \]
This means that \( x = -12 \) is the value that makes the denominator zero, and thus it is excluded from the domain.
The domain will be all real numbers except \( -12 \). We can express this in interval notation:
\[ (-\infty, -12) \cup (-12, \infty) \]
Thus, the correct choice is:
O A. The domain of f(x) is restricted to \((- \infty, -12) \cup (-12, \infty).\)