Determine whether the functions f and g are inverses of each other.
-$f ( x ) = ( x + 7 ) ^ { 3 } + 4 ; g ( x ) = \sqrt [ 3 ] { x - 4 } - 7$

Question

Quizplus · Accepted Answer

To determine if $f$ and $g$ are inverses, we check if $g(f(x)) = x$ and $f(g(x)) = x$. Substituting $f(x)$ into $g$, we get $g(f(x)) = \sqrt[3]{(x+7)^3 + 4 - 4} - 7 = x$. Substituting $g(x)$ into $f$, we get $f(g(x)) = ((\sqrt[3]{x-4}) - 7 + 7)^3 + 4 = x$. Since both compositions return $x$, $f$ and $g$ are inverses of each other.

Determine Whether the Functions F and G Are Inverses of Each