91Ó°ÊÓ

14) For each of the following expressions state whether or not it is periodic, and, if it is periodic, give the period. (a) \(\frac{\sin x}{x}, \quad x \neq 0\), (b) \(|\sin x|\).

For any real number \(x,[x]\) denotes the greatest integer not exceeding \(x\); e.g. \(\quad[3.6]=3, \quad[2]=2, \quad[-1.4]=-2\), etc. Functions \(f\) and \(g\) are defined on the domain of all real numbers as follows: $$ f: x \rightarrow[x] ; \quad g: x \rightarrow x-[x] $$ Find the ranges of \(f\) and \(g\) and sketch the graph of \(g\). Determine the solution sets of the equations (a) \(f(x)=g(x)\) (b) \(f g(x)=g f(x)\) (U of \(\mathrm{L}\) )