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

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Solution

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

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

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

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

4 $[- 3, - 2) \cup (- 2, - 1) \cup [1, \infty)$

Ans.
(3)

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

$\Rightarrow$ $x^{2} > 1 \Rightarrow - 1 > x > 1$ and $3 + x > 0$ $∴$ $x > - 3$ and $x \neq - 2$

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

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