The domain of the function f(x) = _ 3 + x ( x^2 - 1) is - Vidyadip

MCQ

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

A
$( - 3,\; - 1) \cup (1,\;\infty )$
B
$[ - 3,\; - 1) \cup [1,\;\infty )$
✓
$( - 3,\; - 2) \cup ( - 2,\; - 1) \cup (1,\;\infty )$
D
$[ - 3,\; - 2) \cup ( - 2,\; - 1) \cup [1,\;\infty )$

✓

Answer

Correct option: C.

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

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

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

$\therefore$ $x > - 3$ and $x \ne - 2$

$\therefore$ ${D_f} = ( - 3,\, - 2) \cup ( - 2,\, - 1) \cup (1,\,\infty )$.

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