SOLUTION: explain why a polynomial function of even degree cannot have an inverse.

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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(20850) About Me  (Show Source):
You can put this solution on YOUR website!
first recall the definition of inverse:
A function f with domain D is said to be one_to_one if NO
distinct points in D have same image under f, that is:
f%28x1%29+ is_+not_+equal to f%28x2%29 whenever x1 is_+not_+%0D%0A%0D%0Aequal to x2, and (x1,x2) is element of D.
Why a polynomial function of even degree cannot have an inverse?
Simply, because a polynomial function of even degree is NOT
one_to_one function.
Each value of x squared, raised to 4th degree, or higher even
degree, will be that same value; for example, -2%5E2=+4, and also 2%5E2+=+%0D%0A%0D%0A4. This means that two distinct points in D have same image
under f.

example:
let f%28x%29+=+1+-+x%5E2
let domain D be equal to -3,-1,0,1,3
find f%28-3%29, f%28-1%29,f%280%29,f%281%29,f%283%29

f%28-3%29=+1+-+%28-3%29%5E2=+1+-+9+=+-8
f%28-1%29=+1+-+%28-1%29%5E2=+1+-+1+=+0

f%280%29=+1+-+%280%29%5E2=+1+-+0+=+1
f%281%29=+1+-+%281%29%5E2=+1+-+1+=+0
f%283%29=+1+-+%283%29%5E2=+1+-+9+=+-8
as you can see, f%28-3%29 and f%283%29 have same image under f
also f%28-1%29 and f%281%29 have same image under f