Let $f: R \rightarrow R$ be defined by $f(x) = \left\{\begin{array}{cc} 2x, & x > 3 \\ x^2, & 1 < x \leq 3 \\ 3x, & x \leq 1 \end{array}\right.$. Then,the value of $f(-2) + f(3) + f(4)$ is:

If $f: N \rightarrow Z$ is defined by $f(n)=\begin{cases} 2 & \text{if } n=3k, k \in Z \\ 10 & \text{if } n=3k+1, k \in Z \\ 0 & \text{if } n=3k+2, k \in Z \end{cases}$, then $\{n \in N: f(n)>2\}$ is equal to

Let the function $f:R \to R$ be defined by $f(x) = 2x + \sin x, x \in R$. Then $f$ is

Let $f: R \rightarrow R$ be defined by $f(x) = 5^{-|x|} + \operatorname{sgn}(5^{-x})$, where $\operatorname{sgn}(x)$ denotes the signum function of $x$. Then $f$ is

Let $R$ be the set of all real numbers. Let $f: R \rightarrow R$ be a function defined by $f(x) = \begin{cases} 2x-5 & x < -3 \\ x+2 & -3 \leq x < 5 \\ 3x+1 & x \geq 5 \end{cases}$
Match the following:

List-$I$	List-$II$
$(A) f(-5)+f(0)+f(-1)$	$(I) 16$
$(B) f(f(5)+10f(-3))$	$(II) 40$
$(C) f(f(-4))$	$(III) -31$
$(D) f(f(f(1)))$	$(IV) -12$
	$(V) 19$

The correct match is:

For the mapping $f: R-\{1\} \rightarrow R-\{2\}$, given by $f(x)=\frac{2x}{x-1}$, which of the following is correct?