Let $f_1: R \rightarrow R$,$f_2:[0, \infty) \rightarrow R$,$f_3: R \rightarrow R$ and $f_4: R \rightarrow [0, \infty)$ 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 $I$List $II$
$P. f_4$ is$1. \text{onto but not one-one}$
$Q. f_3$ is$2. \text{neither continuous nor one-one}$
$R. f_2 \circ f_1$ is$3. \text{differentiable but not one-one}$
$S. f_2$ is$4. \text{continuous and one-one}$

Codes: $P \quad Q \quad R \quad S$

  • A
    $3 \quad 1 \quad 4 \quad 2$
  • B
    $1 \quad 3 \quad 4 \quad 2$
  • C
    $3 \quad 1 \quad 2 \quad 4$
  • D
    $1 \quad 3 \quad 2 \quad 4$

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