Question

Let f : R → R be the Signum Function defined as

f(x) = $\{\begin{array}{ll}1,& x>0\\ 0,& x=0\\ -1,& x<0\end{array}$

and g : R → R be the greatest Integer Function given by g(x) = | x |, where | x | is the greatest integer less than or equal to x. Then, does f o g and g o f coincide in (0,1].

Answer 1

f : R → R, the Signum Function is defined as

f(x) = $\{\begin{array}{ll}1,& x>0\\ 0,& x=0\\ -1,& x<0\end{array}$