If f is any rigid motion and T is any translation, identify the rigid motion T o f o T^(-1).
Can I split the f into three reflections since there is a theorem that says "Every rigid motion is the composition of at most three relfections and every rigid motion is a translation, a rotation, or a glide relfection"?
My intuition tells me that the final answer would be f by itself since T o T^(-1) will be cancelled out ... I just guess.
If you don't mind me asking, what class is this for?? Some of your questions suggest you're in an introductory analysis course...but....what's with all the isometry/rigid motion questions? I mean, a couple are a nice supplement to a discussion of mappings but the majority of your questions are these.