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) $\mathrm { No }$

Question

Quizplus · Accepted Answer

To determine if $f$ and $g$ are inverses of each other, we check if $f(g(x)) = x$ and $g(f(x)) = x$. For $f(x) = x^3 + 8$ and $g(x) = \sqrt[3]{x - 8}$, we find $f(g(x)) = (\sqrt[3]{x - 8})^3 + 8 = x - 8 + 8 = x$ and $g(f(x)) = \sqrt[3]{(x^3 + 8) - 8} = \sqrt[3]{x^3} = x$. Since both compositions return $x$, $f$ and $g$ are inverses of each other.

Determine Whether the Functions F and G Are Inverses of Each