Question

what is the domain of $f(x) = \frac{3x}{x - 1}$? all real numbers except 3 all real numbers except 1 all real numbers all nonzero numbers

Explanation:

Step1: Recall domain of rational functions

For a rational function \( f(x)=\frac{g(x)}{h(x)} \), the domain excludes values where \( h(x) = 0 \) (since division by zero is undefined).

Step2: Find where denominator is zero

Given \( f(x)=\frac{3x}{x - 1} \), set the denominator \( x-1=0 \). Solving \( x - 1=0 \) gives \( x = 1 \). So \( x = 1 \) makes the denominator zero and is excluded from the domain. The domain is all real numbers except \( x = 1 \).

Answer:

all real numbers except 1