To determine if the cubic function \( y = x^3 \) and the cube root function \( y = \sqrt[3]{x} \) are inverses, we need to check if the composition of the two functions yields the identity function.
- First check: Composition of \( f \) and \( g \)
- Let \( f(x) = x^3 \) (the cubic function) and \( g(x) = \sqrt[3]{x} \) (the cube root function).
- Compute \( g(f(x)) = g(x^3) = \sqrt[3]{x^3} = x \).
- Now compute \( f(g(x)) = f(\sqrt[3]{x}) = (\sqrt[3]{x})^3 = x \).
Since both compositions yield the identity function \( x \), we confirm that the cubic function and the cube root function are indeed inverses of each other.
Thus, the correct response is:
Yes, all corresponding ordered pairs are reflections of one another across the line \( y = x \).