Final Answer:
The inverse graph of $f(x) = x³$ is represented by option B) $y = x^{1/3}$.
Step-by-step explanation:
The inverse function undoes the operation of the original function, swapping the roles of input and output. To find the inverse of $f(x) = x³$, we switch $x$ and $y$ and solve for $y$:
1. Start with the original function: $y = x³$.
2. Swap $x$ and $y$: $x = y³$.
3. Solve for $y$: $y = x^{1/3}$.
This reveals that the inverse function is $y = x^{1/3}$, corresponding to option B.
The cube root function, $y = x^{1/3}$, is indeed the inverse of $f(x) = x³$. When you compose these functions, $f\left(x^{1/3}\right) = \left(x^{1/3}\right)³ = x$. This confirms the inverse relationship. Option A) $y = \sqrt[3]{x}$ is not equivalent to $y = x^{1/3}$; the square root and cube root are distinct operations. Options C) $y = x²$ and D) $y = x^{-3}$ are not inverses; one represents squaring, and the other represents raising to the power of -3, neither of which undoes the cube operation. Therefore, the correct answer is B) $y = x^{1/3}$.