Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injections that can be defined from $A$ to $B$ is

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

$A = \{1, 2, 3, 4\}$ and $B = \{1, 2, 3, 4, 5, 6\}$ are two sets, and the function $f: A \rightarrow B$ is defined by $f(x) = x + 2$ for all $x \in A$. Then the function $f$ is:

Function $f: R \rightarrow R$ defined by $f(x) = x^3$ is . . . . . . .

If $f: R \rightarrow R$ is defined by $f(x)=x-[x]-\frac{1}{2}$ for $x \in R$, where $[x]$ is the greatest integer not exceeding $x$, then $\{x \in R: f(x)=\frac{1}{2}\}$ is equal to :

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