Quote:
Originally Posted by S485122
(For instance it is obvious that x=y^{3} is not the inverse function of y=x^{3}, since substituting x for your inverse function will give y=(y^{3})^{3}=x^{9}.)
Jacob

If you rewrite x = y
^{3} to be in the format of y as a function of x, then the definition you cite applies. You're splitting hairs to say that y = x
^{1/3} is the inverse, but x = y
^{3} is not.
To find an inverse, switch x and y. If you want the inverse in g(x) format, then solve for y after switching x and y.