Describe explicitly all the automorphisms of an affine line $\mathbb A^1.$

Question

Describe explicitly all the automorphisms of an affine line $\mathbb A^1.$

$k[\mathbb A^1]=K[x]$, hence, $\textrm{Aut}_K(k[\mathbb A^1])=\{ax+b|a,b\in K\:\&\:a\ne0\}.$ I am not sure about the word 'explicitly'. As far as I understand, automorphisms of $\mathbb A^1$ are dual to the mentioned ones. Is it possible to somehow make the description more explicit?

Answer 1

I assume you have a proof showing that the only automorphisms of the affine line are linear polynomials. If so, this is as explict as it possibly gets (as, in particular, the inverses of these linear polynomials are themself linear polynomials so already covered by the description).