question_answer

Let \[{{f}_{1}}:R\to R,\] \[{{f}_{2}}:[0,\,\,\infty )\to R,\] \[{{f}_{3}}:R\to R\] and \[{{f}_{4}}:R\to [0,\infty ),\] be defined by \[{{f}_{1}}(x)=\left\{ \begin{matrix}    |x|, & if\,\,x<0  \\    {{e}^{x}}, & if\,\,x\ge 0  \\ \end{matrix} \right.\], \[{{f}_{2}}(x)={{x}^{2}};\] \[{{f}_{3}}(x)=\left\{ \begin{matrix}    \sin x, & if\,\,x<0  \\    x, & if\,\,x\ge 0  \\ \end{matrix} \right.\] and \[{{f}_{4}}\,\,(x)=\left\{ \begin{matrix}    {{f}_{2}}\,\,({{f}_{1}}\,\,(x)), & if\,\,x<0  \\    {{f}_{2}}\,\,({{f}_{1}}\,\,(x))-1, & if\,\,x\ge 0  \\ \end{matrix} \right.\] Based on above information match the following:

Column I		Column II
a.	\[{{f}_{2}}\,\,\text{of}\,\,{{f}_{1}}\] is	(p)	Onto but not one-one
b.	\[{{f}_{3}}\] is	(q)	Neither continuous nor one ?one
c.	\[{{f}_{2}}\] is	(r)	Differentiable but not one-one
d.	\[{{f}_{4}}\] is	(s)	Continuous and one-one

A)  \[a-q,\,\,b-p,\,\,c-r,\,\,d-s\]

B)  \[a-p,\,\,b-r,\,\,c-q,\,\,d-s\]

C)  \[a-q,\,\,b-r,\,\,c-s,\,\,d-p\]

D)  \[a-p,\,\,b-r,\,\,c-s,\,\,d-q\]

E)  None of these