Let f_1:R\toR,f_2:[0,\infty)\toR,f_3:R\toR and f_4:R\to[0,\infty) be defined by f_1(x)=\{\table|x|,\text{if},x<0;e^x,\text{if},x\geq0; f_2(x)=x^2; f_3(x)=\{\table \sin x,\text{if},x<0;x,\text{if},x\geq 0and f_4(x)=\{\table f_2(f_1(x)),\text{if},x<0;f_2(f_1(x))-1,\text{if},x\geq0 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 o f_1 is (3) differentiable but not one-one (S) f_2 is (4) continuous and one-one [JEE Adv 2014 P2]

Functions

Section: Mathematics

Question : 1 of 30

Marks: +1, -0

Let f1:R→R,f2:[0,∞)→R,f3:R→R and f4:R→[0,∞) be defined by
f1(x)={

|x|,if,x<0;ex,if,x≥0; f2(x)=x2;
f3(x)={

sinx	if	x<0
x	if	x≥0

and f4(x)={

f2(f1(x))	if	x<0
f2(f1(x))−1	if	x≥0

List-I		List-II
(P)	f4 is	(1)	onto but not one-one
(Q)	f3 is	(2)	neither continuous nor one-one
(R)	f2 o f1 is	(3)	differentiable but not one-one
(S)	f2 is	(4)	continuous and one-one

[JEE Adv 2014 P2]

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