Respuesta :

arodri04

Answer:

(x1,y1) = (1, 2)

(x2,y2) = (-1,0)

Step-by-step explanation:

Given: f(x) = x²(x + 1) and g(x) = x + 1

To find the intersection, then set functions equal to each other to solve for x first.

x²(x + 1) =  x + 1; divide by (x+1) from both sides

[tex]x^{2}[/tex] = 1; take the square root to both sides

x = ±1;

The graphs intersect at two points (x1,y1) and (x2,y2)

Use x=1

f(1) = x²(x + 1) = [tex]1^{2}[/tex](1+1) = 2

g(1) = x + 1 = 1 + 1 = 2

(x1,y1) = (1, 2)

Use x= -1

f(-1) = x²(x + 1) = [tex](-1)^{2}[/tex](-1+1) = 0

g(-1) = x + 1 = -1 + 1 = 0

(x2,y2) = (-1,0)

boffeemadrid

The points of intersection of two functions are required.

The points of intersection are [tex](-1,0)[/tex] and [tex](1,2)[/tex].

The given functions are

[tex]f(x)=x^2(x+1)[/tex]

[tex]g(x)=x+1[/tex]

Equating them with each other

[tex]x^2(x+1)=x+1\\\Rightarrow x^2=\dfrac{x+1}{x+1}\\\Rightarrow x^2=1\\\Rightarrow x=\pm 1[/tex]

Substitute the [tex]x[/tex] value in one of the functions.

[tex]x=1[/tex]

[tex]f(1)=1(1+1)=2[/tex]

[tex](1,2)[/tex]

[tex]x=-1[/tex]

[tex]f(-1)=(-1)^2(-1+1)=0[/tex]

[tex](-1,0)[/tex]

The points of intersection are [tex](-1,0)[/tex] and [tex](1,2)[/tex].

Learn more:

https://brainly.com/question/16276433

https://brainly.com/question/11604425

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