Page 63 - ISC-12

Matching-List & Matching-Matrix Type Jai Baba Ki5

5. Let f 1 : R → R, f 2 : [0, ∞) → R, f 3 : R → R and f 4 : R → [0, ∞) be defined by
(
|x| if x < 0,
f 1 (x) =
e x if x ≥ 0;

2
f 2 (x) = x ;
(
sin x if x < 0,
f 3 (x) =
x if x ≥ 0
(
f 2 (f 1 (x)) if x < 0,
and f 4 (x) =
f 2 (f 1 (x)) − 1 if x ≥ 0.

List-I List-II

(P) f 4 is (1) onto but not one-one

(Q) f 3 is (2) neither continuous nor one-one

(R) f 2 ◦ f 1 is (3) differentiable but not one-one

(S) f 2 is (4) continuous and one-one

(P) (Q) (R) (S)

(A) (3) (1) (4) (2)

(B) (1) (3) (4) (2)

(C) (3) (1) (2) (4)
(D) (1) (3) (2) (4)

[JEE 2014]