Let $f$ and $g$ be increasing and decreasing functions,respectively,from $[0, \infty)$ to $[0, \infty)$. Let $h(x) = f(g(x))$. If $h(0) = 0$,then $h(x) - h(1)$ is:

Let $f(x)$ and $g(x)$ be two continuous functions defined from $R \rightarrow R$,such that $f(x_1) > f(x_2)$ and $g(x_1) < g(x_2)$ for all $x_1 > x_2$. Then the solution set of $f(g(\alpha^2 - 2\alpha)) > f(g(3\alpha - 4))$ is

Let $R = \{(1, 3), (2, 2), (3, 2)\}$ and $S = \{(2, 1), (3, 2), (2, 3)\}$ be two relations on set $A = \{1, 2, 3\}$. Then $RoS =$

Let $A = \{1, 2, 3, 5, 8, 9\}$. Then the number of possible functions $f : A \rightarrow A$ such that $f(m \cdot n) = f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to $...............$.

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

If $f: R \setminus \{0\} \rightarrow R$ is defined by $f(x) = x + \frac{1}{x}$,then the value of $(f(x))^2 =$