Question: For each of the following functions, determine the domain of the function.
a. f(x) = 3/(x^2 - 1)
1. **State the problem:** We need to find the domain of the function $$f(x) = \frac{3}{x^2 - 1}$$.
2. **Recall the domain rules:** The domain of a function includes all real numbers for which the function is defined. Since this function is a rational function, it is undefined where the denominator is zero.
3. **Set the denominator not equal to zero:**
$$x^2 - 1 \neq 0$$
4. **Solve for $x$:**
$$x^2 \neq 1$$
$$x \neq \pm 1$$
5. **Interpretation:** The function is undefined at $x = 1$ and $x = -1$ because the denominator becomes zero.
6. **Write the domain:**
The domain is all real numbers except $x = 1$ and $x = -1$.
In interval notation:
$$(-\infty, -1) \cup (-1, 1) \cup (1, \infty)$$