Question

Domain of definition of the function

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

• A. (1, 2)
• B. (–1, 0) ∪ (1, 2)
• C. (1, 2) ∪ (2, $\infty$)
• D. (–1, 0) ∪ (1, 2) ∪ (2, $\infty)$

Answer 1

Answer: (D)

(–1, 0) ∪ (1, 2) ∪ (2, $\infty)$

Answer 2

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

So, $4 - x^{2} \neq 0$ ⇒ $x \neq \pm \sqrt{4} \Rightarrow x \neq \pm 2$

and $x^{3} - x > 0 \Rightarrow x(x^{2} - 1) > 0$ ⇒ $x > 0,|x| > 1$

∴ $D = ( - 1,0) \cup (1,\infty) - \{ 2\}$

$D = ( - 1,0) \cup (1,2) \cup (2,\infty)$.