al-numbers-evaluate-the-correctness-of-this-claim-and-choose-the-best-assessment

Question

A student claims the function f(x) = $$x^{3}$$ 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.

Accepted Answer

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.

Answer

f(x) = $$x^{3}$$ has a restricted domain, while g(x) = ∛x does not, so their domains differ.

Answer

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

Answer

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

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.

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.