To find the domain of the function \( f(x) = \frac{7x}{x - 3} \), we need to determine the values of \( x \) for which the function is defined.
The function is a rational function, and it will be undefined when the denominator is equal to zero. Therefore, we set the denominator equal to zero and solve for \( x \):
\[ x - 3 = 0 \]
Solving this gives:
\[ x = 3 \]
This means that the function is undefined at \( x = 3 \).
The domain of \( f(x) \) consists of all real numbers except \( x = 3 \). In interval notation, the domain can be expressed as:
\[ (-\infty, 3) \cup (3, \infty) \]
So, the domain of the function \( f(x) = \frac{7x}{x - 3} \) is \( (-\infty, 3) \cup (3, \infty) \).