Use composition to verify whether or not the inverse is correct.
-$$f ( x ) = x ^ { 3 } + 8 , f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 8 }$$

Question

Quizplus · Accepted Answer

The correct inverse function should be $f^{-1}(x) = \sqrt[3]{x - 8}$, because when you compose $f(f^{-1}(x))$ or $f^{-1}(f(x))$, you should get $x$ back. In this case, $f(f^{-1}(x)) = (\sqrt[3]{x - 8})^3 + 8 = x$, which verifies the correct inverse, not the provided one.

Use Composition to Verify Whether or Not the Inverse Is f(x)=x3+8,f−1(x)=x+83f ( x ) = x ^ { 3 } + 8 , f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 8 }f(x)=x3+8,f−1(x)=3x+8​

Use Composition to Verify Whether or Not the Inverse Is $f ( x ) = x ^ { 3 } + 8 , f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 8 }$