If $f ( x ) = x ^ { 3 } - 5$ and $g ( x ) = \sqrt [ 3 ] { x + 5 }$, then which of the following is/are true?
A) $( f \circ g ) ( x ) = x$ and $( g \circ f ) ( x ) = x$
B) $f$ is the inverse function of $g$
C) $g$ is the inverse function of $f$
D) All of the above are true.

Question

Quizplus · Accepted Answer

The composition $(f \circ g)(x) = f(g(x)) = f(\sqrt[3]{x + 5}) = (\sqrt[3]{x + 5})^3 - 5 = x$, and $(g \circ f)(x) = g(f(x)) = g(x^3 - 5) = \sqrt[3]{(x^3 - 5) + 5} = \sqrt[3]{x^3} = x$, showing that $f$ and $g$ are inverse functions of each other. This means both A and B are true, and since $f$ is the inverse of $g$, C is also true, making D the correct answer.

If f(x)=x3−5f ( x ) = x ^ { 3 } - 5f(x)=x3−5

If $f ( x ) = x ^ { 3 } - 5$