If $R$ denotes the set of all real numbers,then the function $f: R \to R$ defined by $f(x) = [x]$ is:

Let $f: \mathbb{Z} \rightarrow \mathbb{Z}$ be defined by $f(x) = x^3 + 2$. Then,$f$ is . . . . . . .

Let $f : N \rightarrow N$ be defined by $f(n) = \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases}$ for all $n \in N$. State whether the function $f$ is bijective. Justify your answer.

If $f: R \rightarrow R$ is defined by $f(x)=2x+\sin x, x \in R$, then $f$ is

If $f: Z \rightarrow N$ is defined by $f(n) = \begin{cases} 2n, & \text{if } n > 0 \\ 1, & \text{if } n = 0 \\ -2n-1, & \text{if } n < 0 \end{cases}$, then the function $f$ 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: