Final answer:
The domain of the function is all real numbers excluding x = 1. The range of the function is all real numbers.
Step-by-step explanation:
The domain of a function consists of all the possible values of the independent variable (x) for which the function is defined. The range of a function consists of all possible values of the dependent variable (y) that the function takes as input.
In this case, the function is defined as f(x) = 2x / (3x^2 - 3). To determine the domain, we need to consider the values of x for which the denominator is not equal to zero. Therefore, we need to find the values of x that make the expression 3x^2 - 3 not equal to zero. Solving this inequality gives us x ≠ 1.
So, the domain of the function is all real numbers excluding x = 1. As for the range, since the function is a rational function, its range will be all real numbers except for the y-value which would make the denominator equal to zero. In this case, the denominator will never be equal to zero, so the range of the function is all real numbers.