A student claims the function f(x) = x³ and g(x) = ∛x are identical because both have domain and range all real numbers. Evaluate the correctness of this claim and choose the best assessment.

f(x) = x³ has a restricted domain, while g(x) = ∛x does not, so their domains differ.

They are different functions (one cubic, one cube root), but both are continuous with domain and range equal to all real numbers; thus, the student is correct about domain and range but incorrect about them being identical.

They are identical because they produce the same output for every real input.

f is even and g is odd; therefore, they cannot share domain and range properties.