First slide

Functions (XII)

Question

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

Moderate

A

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

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

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

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

Solution

$f (x) is to be defined when x^{2} - 1 > 0 and 3 + x > 0 and$ $3 + x \neq 1, i.e.,$
$x^{2} > 1 and x > - 3 and x \neq - 2$
$i.e., x < - 1 or x > 1 and x > - 3 and x \neq - 2$
$∴ D_{f} = (- 3, - 2) \cup (- 2, - 1) \cup (1, \infty)$

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