First slide

Functions (XII)

Question

The domain of $f (x) = \frac{3}{4 - x^{2}} + \log_{10} (x^{3} - x)$ is

Moderate

A

(1, 2)
B

$(- 1, 0) \cup (1, 2)$
C

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

$(- 1, 0) \cup (1, 2) \cup (2, \infty)$

Solution

$\frac{3}{4 - x^{2}} + \log_{10} (x^{3} - x)$ is defined
$\Rightarrow 4 - x^{2} \neq 0, x^{3} - x > 0 \Rightarrow x \neq \pm 2,$
$(x + 1) x (x - 1) > 0$
$∴ domain = (- 1, 0) \cup (1, 2) \cup (2, \infty)$

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