Let $N$ be the set of natural numbers. Define a function $f: N \rightarrow N$ by $f(x) = 2x + 1$. Using this definition,complete the table given below.

$x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$y$	$f(1) = \dots$	$f(2) = \dots$	$f(3) = \dots$	$f(4) = \dots$	$f(5) = \dots$	$f(6) = \dots$	$f(7) = \dots$

If $f$ is a relation from the set of positive real numbers to the set of positive real numbers defined by $f(x) = 3x^2 - 2$,then $f$ is

If $Q$ denotes the set of all rational numbers and $f\left(\frac{p}{q}\right)=\sqrt{p^2-q^2}$ for any $\frac{p}{q} \in Q$, then observe the following statements.
$I$. $f\left(\frac{p}{q}\right)$ is real for each $\frac{p}{q} \in Q$.
$II$. $f\left(\frac{p}{q}\right)$ is a complex number for each $\frac{p}{q} \in Q$.
Which of the following is correct?

Let $A = \{1, 2, 3, 4\}$,$B = \{1, 5, 9, 11, 15, 16\}$ and $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$. Is $f$ a function from $A$ to $B$? Justify your answer.

The number of relations $R$ from an $m$-element set $A$ to an $n$-element set $B$ satisfying the condition $(a, b_1) \in R, (a, b_2) \in R \Rightarrow b_1 = b_2$ for $a \in A, b_1, b_2 \in B$ is

Which of the following is $NOT$ a function?