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

1 Answer
Nov 28, 2016

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.