First slide

Functions (XII)

Question

Find the domain of the function $f (x) = \frac{x - 3}{(x + 3) \sqrt{x^{2} - 4}}$

Easy

A

$(- \infty, - 2) \cup (2, \infty)$
B

$(- \infty, - 3] \cup (2, \infty)$
C

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

None of these

Solution

$f (x) = \frac{x - 3}{(x + 3) \sqrt{x^{2} - 4}}$
$We must have x^{2} - 4 > 0 and x \neq - 3$
$Therefore, domain is x \in (- \infty, - 3) \cup (- 3, - 2) \cup (2, \infty) .$

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