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 fog and gof coincide in (0,1]

Explanation

To determine whether \( f \circ g \) and \( g \circ f \) coincide in the interval \( (0, 1] \), we need to analyze both compositions step by step.

### Step 1: Define the Functions
The Signum Function \( f: \mathbb{R} \to \mathbb{R} \) is defined as:
\[
f(x) =
\begin{cases}
1 & \text{if } x > 0 \\
...