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JEE Main 2019
Inverse Trigonometric Functions
Inverse Trigonometric Functions
Easy

Question

Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x)=sec⁡−1(2[x]+1)f(x) = \sec^{-1}(2[x] + 1) is:

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Solution

2[x]+1≤−1 or 2[x]+1≥1⇒[x]≤−1∪[x]≥0⇒x∈(−∞,0)∪x∈[0,∞)⇒x∈(−∞,∞)\begin{aligned} & 2[\mathrm{x}]+1 \leq-1 \text { or } 2[\mathrm{x}]+1 \geq 1 \\ & \Rightarrow[\mathrm{x}] \leq-1 \cup[\mathrm{x}] \geq 0 \\ & \Rightarrow \mathrm{x} \in(-\infty, 0) \cup \mathrm{x} \in[0, \infty) \\ & \Rightarrow \mathrm{x} \in(-\infty, \infty) \end{aligned}

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