If the derivative of `f(x)w.r.t.x` is `(1/2-sin^2x)/f(x)` then f(x) is a periodic function with fundamental period

If f(x) is a periodic function with period T, then

If f(x) is periodic function with period, T, then

If f(x) is periodic function with period, T, then

If f(x) is periodic function with period, T, then

Let f(x) and g(x) be two functions such that g(x)=([x]f(x))/([x]f(x)) and g(x) is a periodic function with fundamental time period 'T', then minimum value of 'T is

Let f(x)=x(2-x), 0 le x le 2 . If the definition of 'f' is extended over the set R-[0, 2] by f(x+1)=f(x) then f is a periodic function with period.

If f'(x)=(1-2sin^(2)x)/(f(x)),(f(x)ge0,AAxinR "and" f(0)=1) then f(x) is a periodic function with the period

If f(x)=[2x+1]+[2-2x]+{x}+{-x} where [.] represents greatest integer function and {.} represents fractional function then (1) f(x) is a periodic functional with fundamental period =1 (2) f(x) has no fundamental period (3) Range of f(x) is {3,4} (4) Range of f(x) is {3}