Question

Si
$f(x + 1) = x(x + 2)$
¿Cuál es el valor de
$f(x) - f(x + 2)$
?
Ayuda por favor!!! ​

Answer 1

Respuesta:

f(x) - f(x + 2) = - 4(x + 1)

Explicación paso a paso:

f(x + 1) = x(x + 2)

f((x - 1) + 1) = (x - 1)((x - 1) + 2)

f(x) = (x - 1)(x + 1)

f(x + 2) = ((x + 2) - 1)((x + 2) + 1)

f(x + 2) = (x + 1)(x + 3)

f(x) - f(x + 2) = (x - 1)(x + 1) - (x + 1)(x + 3)

f(x) - f(x + 2) = x² - 1 - (x² + 3x + x + 3)

f(x) - f(x + 2) = x² - 1 - (x² + 4x + 3)

f(x) - f(x + 2) = x² - 1 - x² - 4x - 3

f(x) - f(x + 2) = - 4x - 4

f(x) - f(x + 2) = - 4(x + 1)