SOLUTION: Let f(x)=2kx +9, where k is a real number. If f(3):f(6)=1:3, determine the value of f(9)-f(3).

Algebra ->  Functions -> SOLUTION: Let f(x)=2kx +9, where k is a real number. If f(3):f(6)=1:3, determine the value of f(9)-f(3).      Log On


   

Question 32173:
Let f(x)=2kx +9, where k is a real number. If f(3):f(6)=1:3, determine the value of f(9)-f(3).
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Need to determine "k".
f(3)=2k(3)+9=6k+9
f(6)=2k(6)+9=12k+9
Then, because f(3):f(6)=1:3, you have the following:
f(3)/f(6)=(6k+9)/(12k+9)=1/3
18k+27=12k+9
6k=-18
k=-3
Now that we have k we know f(x)=-6x+9
So, f(9)=-54+9=-45
And, f(3)=-18+9=-9
So, f(9)-f(3)=-36
Cheers,
Stan H.