Como puedo obtener la función inversa de la siguiente función cuadrática:
f(x)=x^2+4x+2
Respuestas a la pregunta
Respuesta:
1
En general, dado ax2+bx+ca{x}^{2}+bx+cax2+bx+c, la forma factorizada es:
a(x−−b+b2−4ac2a)(x−−b−b2−4ac2a)a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})
a(x−2a−b+b2−4ac
)(x−2a−b−b2−4ac
)
2
En este caso, a=1a=1a=1, b=4b=4b=4 y c=2c=2c=2.
(x−−4+42−4×22)(x−−4−42−4×22)(x-\frac{-4+\sqrt{{4}^{2}-4\times 2}}{2})(x-\frac{-4-\sqrt{{4}^{2}-4\times 2}}{2})
(x−2−4+42−4×2
)(x−2−4−42−4×2
)
3
Simplifica.
(x−−4+222)(x−−4−222)(x-\frac{-4+2\sqrt{2}}{2})(x-\frac{-4-2\sqrt{2}}{2})
(x−2−4+22
)(x−2−4−22
)
4
Extrae el factor común 222.
(x−−2(2−2)2)(x−−4−222)(x-\frac{-2(2-\sqrt{2})}{2})(x-\frac{-4-2\sqrt{2}}{2})
(x−2−2(2−2
))(x−2−4−22
)
5
Mueve el símbolo negativo a la izquierda.
(x−(−2(2−2)2))(x−−4−222)(x-(-\frac{2(2-\sqrt{2})}{2}))(x-\frac{-4-2\sqrt{2}}{2})
(x−(−22(2−2
)))(x−2−4−22
)
6
Cancela 222.
(x−(−(2−2)))(x−−4−222)(x-(-(2-\sqrt{2})))(x-\frac{-4-2\sqrt{2}}{2})
(x−(−(2−2
)))(x−2−4−22
)
7
Eliminar paréntesis.
(x−(−2+2))(x−−4−222)(x-(-2+\sqrt{2}))(x-\frac{-4-2\sqrt{2}}{2})
(x−(−2+2
))(x−2−4−22
)
8
Eliminar paréntesis.
(x+2−2)(x−−4−222)(x+2-\sqrt{2})(x-\frac{-4-2\sqrt{2}}{2})
(x+2−2
)(x−2−4−22
)
9
Extrae el factor común 222.
(x+2−2)(x−−2(2+2)2)(x+2-\sqrt{2})(x-\frac{-2(2+\sqrt{2})}{2})
(x+2−2
)(x−2−2(2+2
))
10
Mueve el símbolo negativo a la izquierda.
(x+2−2)(x−(−2(2+2)2))(x+2-\sqrt{2})(x-(-\frac{2(2+\sqrt{2})}{2}))
(x+2−2
)(x−(−22(2+2
)))
11
Cancela 222.
(x+2−2)(x−(−(2+2)))(x+2-\sqrt{2})(x-(-(2+\sqrt{2})))
(x+2−2
)(x−(−(2+2
)))
12
Eliminar paréntesis.
(x+2−2)(x−(−2−2))(x+2-\sqrt{2})(x-(-2-\sqrt{2}))
(x+2−2
)(x−(−2−2
))
13
Eliminar paréntesis.
(x+2−2)(x+2+2)(x+2-\sqrt{2})(x+2+\sqrt{2})
(x+2−2
)(x+2+2
)
Explicación paso a paso: