Question

consider the following function:

\\f(x) = \frac{2x}{3x^2 - 3}\\

what is the domain of the function?

all real numbers
all nonzero real numbers
all real numbers except 2/3
all real numbers except -1 and 1

Explanation:

Identify the condition for the domain

Using the Domain of Rational Functions knowledge point

$$ 3x^2 - 3 e 0 $$

Solve for the excluded values

Using the Domain of Rational Functions knowledge point

$$
LATEXBLOCK0
$$

State the domain

Using the Domain of Rational Functions knowledge point

$$ x \in \mathbb{R} \setminus \{-1, 1\} $$

Answer:

• all real numbers
• all nonzero real numbers
• all real numbers except 2/3
• all real numbers except -1 and 1 (Correct answer)