**Question:**

A function $f$ from the set of natural numbers to integers defined by

$f(n)=\left\{\begin{array}{l}\frac{n-1}{2}, \text { when } \mathrm{n} \text { is odd } \\ -\frac{n}{2}, \text { when } \mathrm{n} \text { is even }\end{array}\right.$ is

Correct Option: 4

**Solution:**

### Related Questions

Let $R_{1}$ and $R_{2}$ be two relations defined as follows :

$R_{1}=\left\{(a, b) \in \mathbf{R}^{2}: a^{2}+b^{2} \in Q\right\}$ and

$R_{2}=\left\{(a, b) \in \mathbf{R}^{2}: a^{2}+b^{2} \notin Q\right\}$, where $Q$ is the set of all rational numbers. Then :

The domain of the function $f(x)=\sin ^{-1}\left(\frac{|x|+5}{x^{2}+1}\right)$ is $(-\infty,-a] \cup[a, \infty]$. Then $a$ is equal to :

If $R=\left\{(x, y): x, y \in \mathbf{Z}, x^{2}+3 y^{2} \leq 8\right\}$ is a relation on the set of integers $\mathbf{Z}$, then the domain of $R^{-1}$ is :

If $R=\left\{(x, y): x, y \in \mathbf{Z}, x^{2}+3 y^{2} \leq 8\right\}$ is a relation on the set of integers $\mathbf{Z}$, then the domain of $R^{-1}$ is :

Let $f: R \rightarrow R$ be defined by $f(x)=\frac{x}{1+x^{2}}, x \in R$. Then the range of $f$ is :

The domain of the definition of the function $f(x)=\frac{1}{4-x^{2}}+\log _{10}\left(x^{3}-x\right)$ is:

The range of the function $f(x)=\frac{x}{1+|x|}, x \in R$, is is

The domain of the function $f(x)=\frac{1}{\sqrt{|x|-x}}$ is

Domain of definition of the function $f(x)=\frac{3}{4-x^{2}}+\log _{10}\left(x^{3}-x\right)$, is

Let $[t]$ denote the greatest integer $\leq t$. Then the equation in $x,[x]^{2}+2[x+2]-7=0$ has :