Given $f'(x) > 0$ and $g'(x) < 0$ for all $x \in R$,then which of the following is true?

Let $R$ denote the set of all real numbers and $R^{+}$ denote the set of all positive real numbers. For the subsets $A$ and $B$ of $R$,define $f: A \rightarrow B$ by $f(x) = x^2$ for $x \in A$. Match the following lists:
| Column $I$ | Column $II$ |
| :--- | :--- |
| $A$. $f$ is one-one and onto,if | $1$. $A = R^{+}, B = R$ |
| $B$. $f$ is one-one but not onto,if | $2$. $A = B = R$ |
| $C$. $f$ is onto but not one-one,if | $3$. $A = R, B = R^{+}$ |
| $D$. $f$ is neither one-one nor onto,if | $4$. $A = B = R^{+}$ |

If $f: R-\{0\} \rightarrow R$ is defined by $f(x)=x+\frac{1}{x}$ and if $f^k(x)=[f(x)]^k$ for $k \geq 1$,then find the value of $f^4(x)-f(x^4)-4f^2(x)$.

Let $f: \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = 2x + |x|$,then $f(2x) + f(-x) - f(x) = $

If $f(x)=\frac{2^{x}+2^{-x}}{2}$,then $f(x+y) \cdot f(x-y)$ is

Let $f: X \rightarrow Y$ be a function and $A, B$ be non-void subsets of $Y$. Which of the following is true?