JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Let \([x]\) denote the greatest integer less than or equal to \(x\). Then the domain of \(f(x)=\sec ^{-1}(2[x]+1)\) is :
- A \((-\infty,-1] \cup[0, \infty)\)
- B \((-\infty,-1] \cup[1, \infty)\)
- C \((-\infty, \infty)\)
- D \((-\infty, \infty)-\{0\}\)
Answer & Solution
Correct Answer
(C) \((-\infty, \infty)\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{ll} f(x)=\sec ^{-1}(2[x]+1) \\ \Rightarrow 2[x]+1 \geq 1 & \text { or } 2[x]+1 \leq-1 \\ \Rightarrow 2[x] \geq 0 & \text { or } 2[x] \leq-2 \\ \Rightarrow[x] \geq 0 & \text { or }[x] \leq-1 \\ \Rightarrow x \geq 0 & \text { or } x \leq 0 \end{array}\) Domain of…
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