## Function Composition in Mathematica

Hi there,

I've been doing a lot of things with Galois Theory recently, and I have been spending an extreme amount of time composing automorphisms with each other to compute Galois groups. For example, I would like to compose to maps that look like $\sigma: \sqrt{2}\mapsto -\sqrt{2}$.

I was wondering if there is an easy way to get Mathematica to do it, so that I can use my time working on other problems. I would appreciate any suggestions!