Question 110971This question is from textbook
: explain why a polynomial function of even degree cannot have an inverse.
This question is from textbook
Answer by MathLover1(3376) (Show Source):
You can put this solution on YOUR website!first recall the  of inverse:
A function  with domain  is said to be  if
distinct points in  have same  under  , that is:
 to  whenever  to  , and (  ,  ) is element of  .
Why a polynomial function of even degree cannot have an inverse?
Simply, because a polynomial function of even degree is
 function.
Each value of  squared, raised to  degree, or higher even
degree, will be that same value; for example,  , and also  . This means that two distinct points in  have same
under  .
example:
let
let domain  be equal to  ,  ,  ,  ,
find  ,  ,  ,  ,
as you can see,  and  have same image under
also  and  have same image under
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