Question

Let f: R → R and g: C → C be two functions defined as f(x) = x² and g(x) = x². Are they equal functions?

Answer 1

Given as

f: R → R ∈ f(x) = x² and g : R → R ∈ g(x) = x²

f is the defined from R to R, the domain of f = R.

g is the defined from C to C, the domain of g = C.

The two functions are equal only when the domain and co-domain of both the functions are equal.

In this case, the domain of f ≠ domain of g.

Thus, f and g are not equal functions.