Let f : R → R be the Signum Function defined as 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 fog and gof coincide in (0, 1]?

SOLUTION:

Given:

f : R → R be the Signum Function characterized as

also, g : R → R be the Greatest Integer Function given by g (x) = [x], where [x] is

most prominent number not exactly or equivalent to x.

Presently, let say x ∈ (0, 1], then, at that point

[x] = 1 if x =1 and

[x] = 0 if 0< x < 1 Therefore:

Gof(x) = g(f(x)) = g(1) = [1] = 1

For x > 0

At the point when x ∈ (0, 1), then, at that point mist = 0 and gof = 1

In any case, mist (1) ≠ gof (1)

This shows that, haze and gof don’t concide in 90, 1].