If f(x)`={{:(x^(3)+x^(2)quad "for" quad 0lexle2),(x+2 quad"for" quad 2ltxle4):}`. Then find the even and odd extension of f(x)

Find the even extension of f(x)={x^(2)-x^(3),0 =3

If f(x)={{:(3x^(2)+12x-1",",-1lexle2),(37-x",",2ltxle3):} , Then

f(x)={(2|x|+x^(2))/(x),quad x!=00,quad x=0 at x=0

If f(x)={{:(3x-4",",0lexle2),(2x+lamda",",2ltxle3):} is continouous at x=2, then what is the value of lamda ?

f(x)={{:(1+x, if 0lexle2),(3-x if 2ltxle3) :} ,then the number of values of x at which the function fof is not differentiable is

The function f(x) Is defined as follows : f(x)={{:(x^(2)+ax+b" , "0lexlt2),(3x+2" , "2lexle4),(2ax+5b" , "4ltxle8):} . If f(x) is continuous on [0,8], find the values of 'a' and 'b'.

Let f(x)=x^(3)-x^(2)+x+1 and g(x)={("max "f(t) 0letlex 0lexle1),(3-x 1ltxle2):} then

If f(x)=x^(3)+3x^(2)-2x+4, find f(-2)+f(2)-f(0)

If f(x)={{:(x",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):} and g'(x)=f(x), x in [1,3] , then

if f(x)={[x^(3)+x^(2), for 0<=x<=2x+2, for 2