Q. The domain of the function $f(x) = \log_{3 + x}{(x^{2} - 1)}$ is
A) $( - 3,\ - 1) \cup (1,\ \infty)$
B) $\lbrack - 3,\ - 1\rbrack \cup \lbrack 1,\ \infty\rbrack$
C) $( - 3,\ - 2) \cup ( - 2,\ - 1) \cup (1,\ \infty)$
D) $\lbrack - 3,\ - 2) \cup ( - 2,\ - 1) \cup (1,\ \infty)$
Explanation
(c)
The given function is defined when $x^{2} - 1;3 + x > 0$ and $3 + x \neq 1$
$\Rightarrow \ \ \ \ x^{2} > 1;\ \ \ 3 + x > 0$ and $x \neq - 2$
$\Rightarrow \ \ \ \ - 1 > x > 1;\ \ x > - 3$, $\ x \neq - 2$
$\therefore$ Domain of the function is
$D_{f} = ( - 3,\ - 2) \cup ( - 2,\ - 1) \cup (1,\ \infty)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.