JEE Advanced 2014 Paper 2 Mathematics Q20

Mathematics

Problem

Let

f_1:\mathbb R\to\mathbb R

f_2:[0,\infty)\to\mathbb R

f_3:\mathbb R\to\mathbb R

and

f_4:\mathbb R\to[0,\infty)

be defined by

f_1(x)=|x|

x<0

and

f_1(x)=e^x

x\ge0

;

f_2(x)=x^2

;

f_3(x)=\sin x

x<0

and

f_3(x)=x

x\ge0

; and

f_4(x)=f_2(f_1(x))

x<0

and

f_4(x)=f_2(f_1(x))-1

x\ge0

. Match the lists and select the correct option. Column I — P:

f_4

is; Q:

f_3

is; R:

f_2\circ f_1

is; S:

f_2

is Column Ii — 1: onto but not one-one; 2: neither continuous nor one-one; 3: differentiable but not one-one; 4: continuous and one-one