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