AP EAMCET · Maths · Functions
The domain of the real valued function \(f(x)=\frac{3}{4-x^2}+\log _{10}\left(x^3-x\right)\) is
- A \((1,2) \cup(2, \infty)\)
- B \((-1,0) \cup(1,2)\)
- C \((-1,0) \cup(1,2) \cup(2, \infty)\)
- D \((-\infty,-1) \cup(1,2) \cup(2, \infty)\)
Answer & Solution
Correct Answer
(C) \((-1,0) \cup(1,2) \cup(2, \infty)\)
Step-by-step Solution
Detailed explanation
\(4-x^2 \neq 0 \Rightarrow x \neq \pm 2\) \(x^3-x > 0 \Rightarrow x(x^2-1) > 0 \Rightarrow x(x-1)(x+1) > 0\) \(x \in (-1, 0) \cup (1, \infty)\) \(x \in ((-1, 0) \cup (1, \infty)) \setminus \{2\}\) \(x \in (-1, 0) \cup (1, 2) \cup (2, \infty)\)
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