I would like to build a periodic function based on the function x-->x².
For x belonging to [0,2], the function is defined like this :
And for the rest of the domain in R, the function should be periodic with a period of 2.
In other words, I would like to define a function which permits me to obtain this plot :
Sorry, for my picture which is very ugly, but it should enable to explain what I'm looking for.
1) Is a new piecewise function based on f function is the better solution to create this kind of periodic function ?
2) I didn't find or understand with the help how i can create "infinite" piecewise function. May you help me to define this kind of piecewise function ?
Thanks a lot for your help.
P.S: With the term "nested" in my title I only want to say that I want to apply another piecewise function (for example g) on a already created function (for example f). this term may be not very appropriated.