f(x)=[x]is discontinuous at all the integer points. Hence, statement 1 is not correct.
f(x)=sin|x|={
sinx,
x≥0
−sinx,
x<0
sinx is a continuous function for x≥0 −sinx is also a continuous function for x<0 at x=0,LHL=RHL=f(0) Hence, the given function is continuous for all real values of x. Statement 2 is correct.