JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Inverse Trigonometric Functions

Let

[x]

denote the greatest integer less than or equal to x . Then domain of

f (x) = sec^{- 1} (2 [x] + 1)

is :

Answer: (B)

Solution

sec^{- 1} (y)

is defined when

∣ y ∣ \geq 1

. With

y = 2 [x] + 1

2 [x] + 1 \geq 1 ⟺ [x] \geq 0 ⟺ x \geq 0

2 [x] + 1 \leq - 1 ⟺ [x] \leq - 1 ⟺ x < 0

Together these cover every real number, so the domain is all of

R

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