Respuesta :
Answer:
3 and 9
if f(x)=x^2+13 and g(x)=12x-14
Step-by-step explanation:
So when we are looking for the intersection of two functions, we are trying to figure out when they are the same. When you think same, you should think equal (=).
So we want to find when f(x)=g(x) for x.
f(x)=g(x)
[tex]x^2+13=12x-14[/tex]
Let's get everything to one side.
Subtracting 12x and adding 14 to both sides.
[tex]x^2+13+14-12x=0[/tex]
I'm going to reorder the left hand side and also simplify the 13+14 part:
[tex]x^2-12x+27=0[/tex]
Now since the coefficent of x^2 is just 1 our job is to find two numbers that multiply to be 27 and add up to be -12.
Those numbers are -3 and -9 since -3(-9)=27 and -3+(-9)=-12.
So the factored form of our equation is
[tex](x-3)(x-9)=0[/tex]
Since the product is 0, then at least one of the factors must be 0.
So we want to solve both x-3=0 and x-9=0.
x-3=0 can be solved by adding 3 on both sides. This gives us x=3.
x-9=9 can be solved by adding 9 on both sides. This gives us x=9.
The intersection of f and g happens at x=3 or x=9.
Answer:
x = 9 and x = 3
Step-by-step explanation:
Given
f(x) = x² + 13 and g(x) = 12x - 14
To find the points of intersection equate the 2 functions, that is
f(x) = g(x)
x² + 13 = 12x - 14 ← subtract 12x - 14 from both sides
x² - 12x + 27 = 0 ← in standard form
Consider the factors of the constant term ( + 27) which sum to give the coefficient of the x- term ( - 12)
The factors are - 3 and - 9, since
- 3 × - 9 = + 27 and - 3 - 9 = - 12, hence
(x - 3)(x - 9) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 9 = 0 ⇒ x = 9
The functions intersect at x = 3 and x = 9
