Question

Range of f(x) = [1 + sinx] + [cosx – 1] + [tan^-1x] ∀ x ∈[0, 2π], is (where [.] denotes the greatest integer function)

• A. {-1, 1, 2}
• B. {-1, 0, 1}
• C. {-1, 0, 1, 2}
• D. {-1, 0, 2}

Answer 1

Answer: (C)

{-1, 0, 1, 2}

Answer 2

f(x) = [sinx] + [cosx] + [tan⁻¹x]. We get

$f ( x ) = \left\{ \begin{array} { l l } 1 , & x = 0 \\ 0 & , 0 < x < \tan 1 \\ 1 , & \tan 1 \leq x < \pi / 2 \\ 2 , & x = \pi / 2 \\ 0 , & \pi / 2 < x < \pi \\ - 1 , & \pi \leq x < 3 \pi / 2 \pi \\ 0 , & 3 \pi / 2 \leq x < 2 \pi \\ 2 , & x = 2 \pi \end{array} \right.$

Thus range of f(x) = {-1, 0, 1, 2}.