Continuity and Differentiability

Let f: R R and g: R R be functions defined by f(x)= cases x|x| ( 1x ), & x 0, \ 0, & x=0, cases and g(x)= cases 1-2x, & 0 x 12, \ 0, & otherwise. cases Let a,b,c,d R. Define the function h: R R by h(x)=a f(x)+b (g(x)+g ( 12-x ) )+c (x-g(x) )+d g(x), x R. Match each entry in List-I to the correct entry in List-II.

1. (P) → (4) (Q) → (3) (R) → (1) (S) → (2)
2. (P) → (5) (Q) → (2) (R) → (4) (S) → (3)
3. (P) → (5) (Q) → (3) (R) → (2) (S) → (4)
4. (P) → (4) (Q) → (2) (R) → (1) (S) → (3)