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:
[tex]f\left(x\right)=3f\left(x-1_\right)+4[/tex]
[tex]f\left(4\right)=3f\left(3\right)+4=\left(25\times 3\right)+4=75+4=79[/tex]
A function, g, passes through the points (1,36), (2,43) and (3,50).
The g(x) is obtained by:
[tex]g\left(x\right)=g\left(x-1\right)+7[/tex]
[tex]g\left(4\right)=g\left(4-1\right)+7=g\left(3\right)+7=50+7=57[/tex]
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.
