Let $f_1 : \mathbb{R} \rightarrow \mathbb{R}$, $f_2 : [0,\infty) \rightarrow \mathbb{R}$, $f_3 : \mathbb{R} \rightarrow \mathbb{R}$ and $f_4 : \mathbb{R} \rightarrow [0,\infty)$ be defined by $$f_1(x) = \begin{cases} |x| & \text{if } x < 0 \\ e^x & \text{if } x \geq 0 \end{cases}$$ $$f_2(x) = x^2;$$ $$f_3(x) = \begin{cases} \sin x & \text{if } x < 0 \\ x & \text{if } x \geq 0 \end{cases}$$ and $$f_4(x) = \begin{cases} f_2(f_1(x)) & \text{if } x < 0 \\ f_2(f_1(x)) - 1 & \text{if } x \geq 0 \end{cases}$$ List I (functions) P. $f_4$ is Q. $f_3$ is R. $f_2 \circ f_1$ is S. $f_2$ is List II (properties) 1. onto but not one-one 2. neither continuous nor one-one 3. differentiable but not one-one 4. continuous and one-one P Q R S (A) 3142 (B) 1342 (C) 3124 (D) 1324
Let $f_1 : \mathbb{R} \rightarrow \mathbb{R}$, $f_2 : [0,\infty) \rightarrow \mathbb{R}$, $f_3 : \mathbb{R} \rightarrow \mathbb{R}$ and $f_4 : \mathbb{R} \rightarrow [0,\infty)$ be defined by
$$f_1(x) = \begin{cases} |x| & \text{if } x < 0 \\ e^x & \text{if } x \geq 0 \end{cases}$$
$$f_2(x) = x^2;$$
$$f_3(x) = \begin{cases} \sin x & \text{if } x < 0 \\ x & \text{if } x \geq 0 \end{cases}$$
and
$$f_4(x) = \begin{cases} f_2(f_1(x)) & \text{if } x < 0 \\ f_2(f_1(x)) - 1 & \text{if } x \geq 0 \end{cases}$$
\textbf{List I (functions)}\\
P. $f_4$ is\\
Q. $f_3$ is\\
R. $f_2 \circ f_1$ is\\
S. $f_2$ is
\textbf{List II (properties)}\\
1. onto but not one-one\\
2. neither continuous nor one-one\\
3. differentiable but not one-one\\
4. continuous and one-one
P Q R S\\
(A) 3142\\
(B) 1342\\
(C) 3124\\
(D) 1324