Question

Find the domain of the real valued function: f(x) = $\frac{1}{(x^{2} - 1)(x + 3)}$

Answer 1

The $\textbf{domain}$ of function $\textbf{f(x)}$ is the set of all values for which function is defined.

we have to find domain of real values function : f(x) = $\frac{1}{(x^2-1)(x+3)}$

To define f(x), denominator of f(x) ≠ 0

e.g., (x² - 1)(x + 3) ≠ 0

or, (x - 1)(x + 1)(x + 3) ≠ 0

or, x ≠ 1 , -1 , -3

hence, domain of f(x) doesn't include 1, -1 and -3

so, domain of f(x) $\in\mathbb{R}-\{1,-1,-3\}$