Determine whether the functions f and g are inverses of each other.
-$$f ( x ) = x ^ { 3 } + 8 ; g ( x ) = \sqrt [ 3 ] { x } - 8$$
A) Yes
B) No

Question

Quizplus · Accepted Answer

To determine if f and g are inverses, we need to check if f(g(x)) = x and g(f(x)) = x. Calculating f(g(x)) gives $f(\sqrt[3]{x} - 8) = (\sqrt[3]{x} - 8)^3 + 8$, which simplifies to $x - 24\sqrt[3]{x}^2 + 192\sqrt[3]{x} - 512 + 8$, not equal to x. Therefore, f and g are not inverses.

Determine Whether the Functions F and G Are Inverses of Each