Question

The domain of the function $f(x) = \log_{3 + x}(x^{2} - 1)$ is

• A. $( - 3, - 1) \cup (1,\infty)$
• B. $\lbrack - 3, - 1) \cup \lbrack 1,\infty)$
• C. $( - 3, - 2) \cup ( - 2, - 1) \cup (1,\infty)$
• D. $\lbrack - 3, - 2) \cup ( - 2, - 1) \cup \lbrack 1,\infty\rbrack$

Answer 1

Answer: (C)

$( - 3, - 2) \cup ( - 2, - 1) \cup (1,\infty)$

Answer 2

$f(x)$ is to be defined when $x^{2} - 1 > 0$

⇒ $x^{2} > 1,$ ⇒ $x < - 1\text{ or }x > 1$ and $3 + x > 0$

∴ $x > - 3$ and $x \neq - 2$

∴ $D_{r} = ( - 3, - 2) \cup ( - 2, - 1) \cup (1,\infty)$.