let k be a field.

a) show that the mapping

definded by

for fixed

is an automorphism of k[t] which is the identity on k.

b) conversely, let

be an automorphism of k[t] which is the identity on k. Prove that thre exist

with

such that

as in part a)

So I have done part a) but I can't seem to get out of the gate for part b).

I keep reading the problem and only seeing the trivial solution.

The identitiy map is an automorphism so

and

satisfy the above, but I have a feeling that is not what Dummit and Foote had in mind.

A push in the right direction would be great.

Thanks

TES