Question

Let f: R → R be the Signum Function defined as f(x)={ 1, x>0 0, x=0−1, x<1
and g: R→ R be the Greatest Integer Function given by g(x) = [x], where [x] is greatest integer less than or equal to x. Then does fo and of coincide in (0, 1]?

Answer 1

It is given that,

f: R → R is defined as f(x)={ 1, x>0 0, x=0  −1, x<1
Also, g: R → R is defined as g(x) = [x], where [x] is the greatest integer less than or equal to x.

Thus, when x ∈ (0, 1), we have fog(x) = 0 and gof (x) = 1.
Hence, fog and of do not coincide in (0, 1].