The function `f(x) = [x] cos((2x-1)/2) pi` where [ ] denotes the greatest integer function, is discontinuous

Options

A. for each real `x`
B. for each integral point
C. no where
D. at each non-integeral point

Answer

C

Explanation

Doubt full points are integers at `x="n","n" epsilonI`
`f(n)=0`
`X=n,"n"epsilon I f(n)=0`
R.H.L.`=lim_(n rarr0)[n+h]=0=`
L.H.L` =lim_(n rarr0)[n-h]0=0`
Continuous every where