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Dadas las siguientes funciones, resuelve las operaciones indicadas.

[tex]F(X) = 2x^2 - 2 \quad g(X) = x + 5[/tex]

a) [tex]F(X) + g(X)[/tex]

b) [tex]F(X) - g(X)[/tex]

c) [tex]F(X) \cdot g(X)[/tex]

Sagot :

GinnyAnswer
Claro, vamos a resolver las operaciones indicadas paso a paso.

Las funciones dadas son:
[tex]\[ F(x) = 2x^2 - 2 \][/tex]
[tex]\[ G(x) = x + 5 \][/tex]

### a) [tex]\( F(x) + G(x) \)[/tex]

Para encontrar esta suma, simplemente sumamos las dos funciones:
[tex]\[ F(x) + G(x) = (2x^2 - 2) + (x + 5) \][/tex]

Ahora, combinamos los términos semejantes:
[tex]\[ F(x) + G(x) = 2x^2 + x + 3 \][/tex]

Por lo tanto:
[tex]\[ F(x) + G(x) = 2x^2 + x + 3 \][/tex]

### b) [tex]\( F(x) - G(x) \)[/tex]

Para la resta, restamos la función [tex]\( G(x) \)[/tex] de [tex]\( F(x) \)[/tex]:
[tex]\[ F(x) - G(x) = (2x^2 - 2) - (x + 5) \][/tex]

Distribuimos el signo negativo y combinamos términos semejantes:
[tex]\[ F(x) - G(x) = 2x^2 - 2 - x - 5 \][/tex]
[tex]\[ F(x) - G(x) = 2x^2 - x - 7 \][/tex]

Por lo tanto:
[tex]\[ F(x) - G(x) = 2x^2 - x - 7 \][/tex]

### c) [tex]\( F(x) \cdot G(x) \)[/tex]

Para la multiplicación, multiplicamos las dos funciones juntas:
[tex]\[ F(x) \cdot G(x) = (2x^2 - 2) \cdot (x + 5) \][/tex]

Utilizamos la propiedad distributiva para multiplicar:
[tex]\[ F(x) \cdot G(x) = (2x^2 - 2) \cdot x + (2x^2 - 2) \cdot 5 \][/tex]
[tex]\[ F(x) \cdot G(x) = 2x^3 - 2x + 10x^2 - 10 \][/tex]

Por lo tanto:
[tex]\[ F(x) \cdot G(x) = 2x^3 + 10x^2 - 2x - 10 \][/tex]

En conclusión, las respuestas son:
[tex]\[ F(x) + G(x) = 2x^2 + x + 3 \][/tex]
[tex]\[ F(x) - G(x) = 2x^2 - x - 7 \][/tex]
[tex]\[ F(x) \cdot G(x) = (x + 5)(2x^2 - 2) \][/tex]
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