Determine whether the given functions are inverses of each other.
-$$f ( x ) = \sqrt [ 5 ] { x - 3 } , \quad g ( x ) = x ^ { 5 } + 3$$
A)Yes
B)No

Question

Quizplus · Accepted Answer

To determine if $f(x)$ and $g(x)$ are inverses of each other, we can check if $f(g(x)) = x$ and $g(f(x)) = x$. Substituting $g(x)$ into $f(x)$, we get $f(g(x)) = \sqrt[5]{(x^5 + 3) - 3} = \sqrt[5]{x^5} = x$. Similarly, substituting $f(x)$ into $g(x)$, we get $g(f(x)) = (\sqrt[5]{x - 3})^5 + 3 = x - 3 + 3 = x$. Since both compositions return $x$, $f(x)$ and $g(x)$ are indeed inverses of each other.

Determine Whether the Given Functions Are Inverses of Each Other f(x)=x−35,g(x)=x5+3f ( x ) = \sqrt [ 5 ] { x - 3 } , \quad g ( x ) = x ^ { 5 } + 3f(x)=5x−3​,g(x)=x5+3

Determine Whether the Given Functions Are Inverses of Each Other $f ( x ) = \sqrt [ 5 ] { x - 3 } , \quad g ( x ) = x ^ { 5 } + 3$