Explicație pas cu pas:
20)
[tex]f(k) = \frac{4k + 1}{3} \in \mathbb{Z} \\ [/tex]
[tex](4k + 1)\in \mathbb{\it M_{3}}[/tex]
[tex]\iff (4k + 1)\in \{...; - 6; - 3; 0; 3; 6; 9; ...\} \\ [/tex]
[tex]\implies 4k \in \{...; -7; -4; -1; 2; 5; 8 ; ...\} \\ [/tex]
[tex]k \in \mathbb{Z} \implies k \in \{...; -1; 2;... \}[/tex]
21)
[tex]f(x) = {x}^{2} - {x}^{4}[/tex]
[tex](f○f)(x) = {(f(x))}^{2} - {(f(x))}^{4}[/tex]
[tex](f○f○f)(x) = (f○(f○f))(x) = {((f○f)(x))}^{2} - {((f○f)(x))}^{4}[/tex]
[tex](f○f)(1) = 0 - 0 = 0[/tex]
[tex]\implies (f○f○f)(1) = {0}^{2} - {0}^{4} = 0 \\ [/tex]
