Question

How do you graph the function and its inverse of `f(x)=x^3+1`?

Answer 1

The inserted graph is the same for both. See explanation

Explanation:

graph{x^3+1 [-10, 10, -5, 5]}

graph{(x-1)^(1/3) [-10, 10, -5, 5]}

I advocate the definition of inverse as the one and only for all locally

bijective functions y = f(x) as x = f^(-1)y and the governing equations

for the function operators f and `f^(-1)` are

`f^(-1)(f(x)) = x and f (f^(-1)y) = y`

Accordingly,

if `y=f(x)=x^3+1, x=f^(y)=(y-1)^(1/3)`.

It is the same equation, presented in two explicit forms.

Of course, I am aware that the other definition in common useias

`y=f^(--1)(x) =(x-1)^(1/3)`, swapping `(x, y) to (y, x)`.

Here, the graph is obtained as the mirror image ith respect to the

bisector line y = x.