This topic is linked to null - null.
Y by
Consider
and such that
we clearly see that,
Recall
thus
we can clearly see that as they are each other inverse that
thus let,
Thus we see,
In other words
and
are elements in the group of units of
although since
it is also the group of units of
therefor ![$R[x]^{\times}=R^{\times}$](//latex.artofproblemsolving.com/3/8/5/38514438d37b6a7580a10e38eeaaf71312c045ec.png)
![$f(x)\in R[x]$](http://latex.artofproblemsolving.com/a/1/5/a15dc97c051e81ae9ff0c060eaa4367bc723ccc9.png)
![$f^{-1}(x)\in R[x]$](http://latex.artofproblemsolving.com/8/2/8/82890174983fbcc0bee7ba062cc7d80a4cf1ad50.png)








![$R[x]$](http://latex.artofproblemsolving.com/1/4/d/14de719c0fff2385124cfbcbd01a2dbb7b9b3300.png)


![$R[x]^{\times}=R^{\times}$](http://latex.artofproblemsolving.com/3/8/5/38514438d37b6a7580a10e38eeaaf71312c045ec.png)