Define $f: R \rightarrow R$ by $f(x) = \max \{x+1, 1-x, 2\}$. Then,$f$ is

Show that the function $f: R_* \rightarrow R_*$ defined by $f(x) = \frac{1}{x}$ is one-one and onto,where $R_*$ is the set of all non-zero real numbers. Is the result true if the domain $R_*$ is replaced by $N$ with the co-domain remaining the same as $R_*$?

$f(x) = \log \left( \left( \frac{2x^2 - 3}{x} \right) + \sqrt{\frac{4x^4 - 11x^2 + 9}{|x|}} \right)$ is

Consider the sets $A = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x^2 + y^2 = 25\}$,$B = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x^2 + 9y^2 = 144\}$,$C = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : x^2 + y^2 \leq 4\}$,and $D = A \cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:

Let $A \subseteq R, B \subseteq R$ and $f: A \rightarrow B$ be defined by $f(x)=x^2-3x+2$. If $f$ is a bijection,then

On the set of integers $Z$,define $f: Z \rightarrow Z$ as $f(n) = \begin{cases} \frac{n}{2}, & n \text{ is even} \\ 0, & n \text{ is odd} \end{cases}$. Then $f$ is: