Find the domain of \(f(x) = \frac{x}{3 - x}, x \in R\), the set of real numbers.
Answer Details
The function \(f(x) = \frac{x}{3-x}\) is defined for all real numbers except when the denominator is zero, i.e., when \(3-x=0\). Therefore, the domain of the function is all real numbers except \(x=3\), or in interval notation: \({x : x \in R, x \neq 3}\).
So the correct option is: \({x : x \in R, x \neq 3}\).