Let f(x)=[3+2cos⁡x],x∈−π2,π2 where [.] denotes the greatest integer function. Then  number of points of discontinuity of f(x) is

3≤3+2cos⁡x≤5 for x∈−π2,π2f(x)=[3+2cos⁡x] is discontinuous at those points where 3+2cos⁡x is an integer ∴3+2cos⁡x=3 if __cos⁡x=0 so x=−π2,π2 (not possible) 3+2cos⁡x=4, if cos⁡x=12 ∴x=π3 and −π33+2cos⁡x=5, if cos⁡x=1  so x=0∴ The value of x=3