1. Tardigrade
  2. Question
  3. Mathematics
  4. The range of function f(x)= operatornamesgn( sin x)+ operatornamesgn( cos x)+ operatornamesgn( tan x)+ operatornamesgn( cot x), x ≠ (n π/2)(n ∈ I) is [Note: sgn k denotes signum function of k.]

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Q. The range of function $f(x)=\operatorname{sgn}(\sin x)+\operatorname{sgn}(\cos x)+\operatorname{sgn}(\tan x)+\operatorname{sgn}(\cot x), x \neq \frac{n \pi}{2}(n \in I)$ is
[Note : sgn $k$ denotes signum function of $k$.]

Relations and Functions - Part 2

Solution:

$f(x)=\begin{cases} 4 ; & 0< x< \frac{\pi}{2} \\ -2 ; & \frac{\pi}{2}< x< \pi \\ 0 ; & \pi< x< \frac{3 \pi}{2} \\ -2 ; & \frac{3 \pi}{2}< x< 2 \pi\end{cases}$
$\therefore$ Range of $f(x)=\{-2,0,4\}$