Answer:
F(4) = G(4) and F(12) = G(12) ⇒ answer B
Step-by-step explanation:
* Lets explain the meaning of the common solutions of two equation
- If two equations intersect at one point, (x , y) where x and y have the
same values for both equations
- The point (x , y) belongs to the two graphs
- Ex: If (2 , 3) is a common solution of f(x) and g(x) , then the graphs of
f(x) and g(x) meet each other at the point (2 , 3) that means f(2) = 3
and g(2) = 3
- So f(2) = g(2)
* Lets solve the problem
∵ F(x) = Ix - 6I
∵ G(x) = 0.5 x
∵ The two graphs intersected at points (4 , 2) and (12 , 6)
- That means the two points (4 , 2) and (2 , 6) on the two graphs
∴ F(4) = 2 and G(4) = 2
∴ F(12) = 6 and G(12) = 6
- That means the two points are common solutions for both equations
∴ The solutions of the equation |x - 6|= 0.5 x are x = 4 and x = 12
∴ F(4) = G(4) and F(12) = G(12)
∴ The best reasons which justifies Kiana's conclusion is;
F(4) = G(4) and F(12) = G(12)
- Look to the attached graph to more understanding
- The red graph is F(x)
- The blue graph is G(x)
