Q. Domain of definition of the function $f(x) = \frac{3}{4 - x^{2}} + \log_{10}{(x^{3} - x)}$, is
A) (1, 2)
B) $( - 1,\ 0) \cup (1,\ 2)$
C) $(1,\ 2) \cup (2,\ \infty)$
D) $( - 1,\ 0) \cup (1,\ 2) \cup (2,\ \infty)$
Explanation
(d)
Since, $f(x) = \frac{3}{4 - x^{2}} + \log_{10}{(x^{3} - x)}$
For domain of $f(x)$,
$\ \ \ \ \ \ \ \ \ \ \ \ \ x^{3} - 1 > 0$, $4 - x^{2} \neq 0)$
$\Rightarrow \ \ x(x - 1)(x + 1) > 0$ and $x \neq \pm 2$
$\Rightarrow \ \ x \in ( - 1,\ 0) \cup (1,\ \infty)$, $x \neq \pm 2$
[image:2_image10.emf]
$\Rightarrow \ \ \ x \in ( - 1,\ 0) \cup (1,\ 2) \cup (2,\ \infty)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.