The domain of the functionf(x)=1sinx+sinπ+x where   denotes the fractional part, is

f(x)=1sinx+sinπ+x=1sinx+−sinxNowsinx+−sinx=0       sinx is an integer1 sinx​ is​ not an integerFor f(x) to get definedsinx+−sinx≠0⇒ sinx≠integer⇒ sinx≠±1,0⇒x≠nπ2,n∈IHence, the domain is R−nπ2/n∈I