Degree of Rational Function Field

[jose80]

Hi,

I am trying to find the degree [F_{q^2}(x):F_{q}(x)]$.

Intuitively, I thought it will be 2? but cannot see that

 

[micromass]

What do you mean with that notation?? The index as groups or the index as fields?? If it is the index as groups, then the answer is q. If it is as fields, then the answer is 2.