Let f: R → R and g: C → C be two functions defined as f(x) = x

1.	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» 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.

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»

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.