Conjuntos

1 $A = \{x / x \in \mathbb{N} \text{ e } x = 2k,\ k \in \mathbb{Z}_{+}\}$

2 $B = \{x / x \in \mathbb{N} \text{ e } x = 3k,\ k \in \mathbb{Z}_{+}\}$

3 $C = \{x / x \in \mathbb{N} \text{ e } x = y^{2},\ y \in \mathbb{Z}_{+}\}$

4 $D = \{x / x \in \mathbb{N} \text{ e } x = k^{2} + 1,\ k \in \mathbb{Z}_{+}\}$

Supondo grau $2$, $f(x) = ax^{2} + bx + c$ com $x = 0, 1, 2, \ldots$:

Resolvendo: $a = 1$, $b = 0$, $c = -1$, logo $f(x) = x^{2} - 1$.

Supondo grau $3$, $f(x) = ax^{3} + bx^{2} + cx + d$:

Resolvendo: $a = 1$, $b = 0$, $c = 0$, $d = 2$, logo $f(x) = x^{3} + 2$.