Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
Given f : R → R ∋ f(x) = x2 and g : R → R ∋ g(x) = x2
As f is defined from R to R, the domain of f = R.
As g is defined from C to C, the domain of g = C.
Two functions are equal only when the domain and codomain of both the functions are equal.
In this case, the domain of f ≠ domain of g.
Thus, f and g are not equal functions.