If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$f(x)=3 x^{3}-6$
A) $f^{-1}(x)=\sqrt[3]{\frac{x+6}{3}}$
B) Not one-to-one
C) $f^{-1}(x)=\sqrt[3]{\frac{x-6}{3}}$
D) $f^{-1}(x)=\sqrt[3]{\frac{x}{3}}+6$

Question

Quizplus · Accepted Answer

The function $f(x)=3x^3-6$ is one-to-one because for every x value, there is a unique y value, and its inverse can be found by swapping x and y and solving for y, leading to $f^{-1}(x)=\sqrt[3]{\frac{x+6}{3}}$.

If the Following Defines a One-To-One Function, Find Its Inverse f(x)=3x3−6f(x)=3 x^{3}-6f(x)=3x3−6

If the Following Defines a One-To-One Function, Find Its Inverse $f(x)=3 x^{3}-6$