Decide whether or not the functions are inverses of each other.
-$$f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }$$
A) No
B) Yes

Question

Quizplus · Accepted Answer

To determine if two functions 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 indeed inverses of each other.

Decide Whether or Not the Functions Are Inverses of Each f(x)=x3−8,g(x)=x+83f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }f(x)=x3−8,g(x)=3x+8​

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }$