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.]

Question

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.] (A)  -2,4  (B)  -2,0,4  (C)  -4,-2,0,4  (D)  0,2,4

Tardigrade Admin · Accepted Answer

f(x)= begincases 4 ; 0< x< (π/2) -2 ; (π/2)< x< π 0 ; π< x< (3 π/2) -2 ; (3 π/2)< x< 2 π endcases ∴ Range of f(x)= -2,0,4

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

${- 2, 4}$

${- 2, 0, 4}$

${- 4, - 2, 0, 4}$

${0, 2, 4}$

$f (x) = ⎩ ⎨ ⎧ 4; - 2; 0; - 2; 0 < x < \frac{π}{2} \frac{π}{2} < x < π π < x < \frac{3 π}{2} \frac{3 π}{2} < x < 2 π$
$∴$ Range of $f (x) = {- 2, 0, 4}$

Q. The range of function f(x)=sgn(sinx)+sgn(cosx)+sgn(tanx)+sgn(cotx),x=2nπ​(n∈I) is [Note : sgn k denotes signum function of k.]

{−2,4}

{−2,0,4}

{−4,−2,0,4}

{0,2,4}