gg[x_]:=Piecewise[{{xLog[2-x],0<=x<1}},​​(x-2)Log[x]];​​g[x_]:=gg[Mod[x,2]];​​Plot[{g[x]},{x,0,10}]​​Reduce[{g[x]==0,0<=x<=2026},x,Reals]
Out[]=
2
4
6
8
10
-0.2
-0.1
0.1
0.2
Out[]=
(

1
∈&&0≤

1
≤1012&&x1+2

1
)||(

1
∈&&0≤

1
≤1013&&x2

1
)