Answer:
As the value of x increases, the value of f(x) will eventually exceed the value of g(x) is the correct option.
Step-by-step explanation:
A function, f, passes through the points (1,1), (2,7) and (3,25).
The equation of the function 'f' can be written as:
The f(x) is obtained by:
![f\left(x\right)=3f\left(x-1_\right)+4](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3D3f%5Cleft%28x-1_%5Cright%29%2B4)
![f\left(4\right)=3f\left(3\right)+4=\left(25\times 3\right)+4=75+4=79](https://tex.z-dn.net/?f=f%5Cleft%284%5Cright%29%3D3f%5Cleft%283%5Cright%29%2B4%3D%5Cleft%2825%5Ctimes%203%5Cright%29%2B4%3D75%2B4%3D79)
A function, g, passes through the points (1,36), (2,43) and (3,50).
The g(x) is obtained by:
![g\left(x\right)=g\left(x-1\right)+7](https://tex.z-dn.net/?f=g%5Cleft%28x%5Cright%29%3Dg%5Cleft%28x-1%5Cright%29%2B7)
![g\left(4\right)=g\left(4-1\right)+7=g\left(3\right)+7=50+7=57](https://tex.z-dn.net/?f=g%5Cleft%284%5Cright%29%3Dg%5Cleft%284-1%5Cright%29%2B7%3Dg%5Cleft%283%5Cright%29%2B7%3D50%2B7%3D57)
So, value of f(x) at x = 4 exceeds the value of g(x) at x = 4.
Therefore, as the value of x increases, the value of f(x) will eventually exceed the value of g(x) is the correct option.