Question

The function f(x) = cos x + {x} (where {.} denotes the fractional part function) is

	Periodic with period 1
	Periodic with period π
	Periodic with period 2π
	Not periodic

Answer 1

$$\begin{gathered} Dearstudent, \\ f\left(x\right)=\left\{x\right\}+\cos x \\ Iftherearetwofunction,thenperiodoftheirsumisL.C.Mofperiodsoftwofunction. \\ Periodof\left\{x\right\}is1. \\ Periodof\cos xis2\mathrm{\pi } \\ LCM\hspace{0.17em}of2\mathrm{\pi }\mathrm{and}1\mathrm{is}2\mathrm{\pi } \\ \mathrm{So},\mathrm{period}\mathrm{of}\mathrm{f}\left(\mathrm{x}\right)=\left\{\mathrm{x}\right\}+\mathrm{cosx}\mathrm{is}2\mathrm{\pi } \\ \mathrm{Regards}! \end{gathered}$$