if`f(x)={x^3+x^2,for0lt=xlt=2x+2,for2

Explanation

For even extension `f(x)=f(-x)`
` :. f(x)=f(-x)={((-x)^(3)+(-x)^(2)",",0le -x le2),(-x+2",",2 lt -x le 4):}`
` ={(-x+2",",-4 le x lt -2),(-x^(3)+x^(2)",",-2lex le0):}`
For odd extension,`f(x)= -f(-x)`
` :. f(x)=-f(-x) ={(x-2",",-4 le x lt -2),(x^(3)-x^(2)",",-2lex le0):}`