Question

For the functions below, indicate whether the function is onto, one-to-one, or a bijection: g: ℝ → ℝ, g(x) = x³.

Answer 1

The function g(x) = x³ is a bijection as it is both onto and one-to-one.

Step-by-step explanation:

To determine whether the function g(x) = x³ is onto, one-to-one, or a bijection, we need to consider its properties.

Onto: A function is onto if every element in the codomain (range) has a corresponding element in the domain. In this case, g(x) = x³ has a real number cube root for every real number, making it onto.

One-to-one: A function is one-to-one if each element in the domain corresponds to a unique element in the codomain. Since g(x) = x³ has a unique cube root for every real number, it is one-to-one.

Bijection: A function is a bijection if it is both onto and one-to-one. Therefore, g(x) = x³ is a bijection because it is both onto and one-to-one.