Final answer:
The inverse of the function f(x) = 2/x^3 is found by swapping x and y, and solving for y, which results in the inverse function f^{-1}(x) = (2/x)^(1/3).
Step-by-step explanation:
The student has asked about finding the inverse of the function f(x) = \frac{2}{x^3}. To find the inverse of a function, we swap the x and y variables and solve for y. In this case, we would set y = \frac{2}{x^3} and then swap x and y to get x = \frac{2}{y^3}. We then solve for y by taking the cube root of both sides and then inverting, which yields y = \left(\frac{2}{x}\right)^{\frac{1}{3}}. Therefore, the inverse function is f^{-1}(x) = \left(\frac{2}{x}\right)^{\frac{1}{3}}.