If `f(x)=(-1)^([2/pi]),g(x)=|sinx|-|cosx|,a n dvarphi(x)=f(x)g(x)` (where [.] denotes the greatest integer function), then the respective fundamental periods of `f(x)`,`g(x)`,and `varphi(x)` are (a) `pi,pi,pi` (b) `pi,2pi,pi` `pi,pi,pi/2` (d) `pi,pi/2,pi`

Options

A. `pi, pi, pi`
B. `pi, 2pi, pi`
C. `pi, pi, (pi)/(2)`
D. `pi, (pi)/(2),pi`

Answer

C

Explanation

Clearly, `f(x+pi)=f(x), g(x+pi)=g(x),`
` and phi (x+(pi)/(2))={(-1)f(x)}{(-1)g(x)}=phi(x)`