\(f(x) = x - [x]\) is the fractional part of \(x\). Since \([x+1] = [x] + 1\):

\(f(x+1) = (x+1) - [x+1] = x - [x] = f(x)\)

So it is periodic with period 1.

The others are not periodic: \(\sin\frac{1}{x}\) oscillates faster and faster near 0 with no repeating interval, and \(x\cos x\) and \(x\cos\frac{1}{x}\) grow without bound.

Answer: (A)