Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Determine the elements of the set:

[tex]\[ M = \left\{\left(\frac{x^2-1}{2}\right) \in \mathbb{Z} \mid x \in \mathbb{Z}, -2 \leq x \leq 9\right\} \][/tex]

Sagot :

GinnyAnswer
Claro, procedamos a determinar los elementos del conjunto [tex]\(M\)[/tex].

Paso 1: Definir el rango de [tex]\(x\)[/tex]

El rango de [tex]\(x\)[/tex] se define entre [tex]\(A-2\)[/tex] y 9, donde [tex]\(A\)[/tex] es un valor dado. Supongamos que [tex]\(A = 2\)[/tex].

Por lo tanto, el rango de [tex]\(x\)[/tex] es: [tex]\(A-2 \leq x \leq 9\)[/tex]
[tex]\[2 - 2 \leq x \leq 9\][/tex]
[tex]\[0 \leq x \leq 9\][/tex]

Entonces, [tex]\(x\)[/tex] toma los valores: 0, 1, 2, 3, 4, 5, 6, 7, 8, y 9.

Paso 2: Aplicar la expresión [tex]\(\left( \frac{x^2 - 1}{2} \right)\)[/tex] para cada valor de [tex]\(x\)[/tex]

Vamos a evaluar la expresión para cada [tex]\(x\)[/tex]:

1. Para [tex]\(x = 0\)[/tex]:
[tex]\[\left( \frac{0^2 - 1}{2} \right) = \left( \frac{-1}{2} \right) = -1\][/tex]

2. Para [tex]\(x = 1\)[/tex]:
[tex]\[\left( \frac{1^2 - 1}{2} \right) = \left( \frac{0}{2} \right) = 0\][/tex]

3. Para [tex]\(x = 2\)[/tex]:
[tex]\[\left( \frac{2^2 - 1}{2} \right) = \left( \frac{4 - 1}{2} \right) = \left( \frac{3}{2} \right) = 1\][/tex]

4. Para [tex]\(x = 3\)[/tex]:
[tex]\[\left( \frac{3^2 - 1}{2} \right) = \left( \frac{9 - 1}{2} \right) = \left( \frac{8}{2} \right) = 4\][/tex]

5. Para [tex]\(x = 4\)[/tex]:
[tex]\[\left( \frac{4^2 - 1}{2} \right) = \left( \frac{16 - 1}{2} \right) = \left( \frac{15}{2} \right) = 7\][/tex]

6. Para [tex]\(x = 5\)[/tex]:
[tex]\[\left( \frac{5^2 - 1}{2} \right) = \left( \frac{25 - 1}{2} \right) = \left( \frac{24}{2} \right) = 12\][/tex]

7. Para [tex]\(x = 6\)[/tex]:
[tex]\[\left( \frac{6^2 - 1}{2} \right) = \left( \frac{36 - 1}{2} \right) = \left( \frac{35}{2} \right) = 17\][/tex]

8. Para [tex]\(x = 7\)[/tex]:
[tex]\[\left( \frac{7^2 - 1}{2} \right) = \left( \frac{49 - 1}{2} \right) = \left( \frac{48}{2} \right) = 24\][/tex]

9. Para [tex]\(x = 8\)[/tex]:
[tex]\[\left( \frac{8^2 - 1}{2} \right) = \left( \frac{64 - 1}{2} \right) = \left( \frac{63}{2} \right) = 31\][/tex]

10. Para [tex]\(x = 9\)[/tex]:
[tex]\[\left( \frac{9^2 - 1}{2} \right) = \left( \frac{81 - 1}{2} \right) = \left( \frac{80}{2} \right) = 40\][/tex]

Conclusión:
Los elementos del conjunto [tex]\(M\)[/tex] son los siguientes:
[tex]\[ M = \{-1, 0, 1, 4, 7, 12, 17, 24, 31, 40\} \][/tex]

Así, hemos determinado los elementos del conjunto [tex]\(M\)[/tex] de manera detallada y paso a paso.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.