1. ## Function f(6) ?

1.) the function f(x) has the following properties:

i) f(1) = 1
ii) f(2x) = 4f(x) + 6
iii) f(x+2) = f(x) + 12x + 12

calculate f(6)

2. Originally Posted by rcs
1.) the function f(x) has the following properties:

i) f(1) = 1
ii) f(2x) = 4f(x) + 6
iii) f(x+2) = f(x) + 12x + 12

calculate f(6)
we need to calculate f(6). Since they defined f(x+2), we could calculate f(3). to calculate f(3) we do:

$|f(3) = f(1+2) = f(1)+12(1)+12 = 1+12+12 = 25$
Now to calculate f(6), we use the formula f(2x):
$f(6) = f(2x) = f(2*3) = 4f(3)+6=4(25)+6=106$

3. I would have done that in a slightly different order: f(6)= f(4+ 2)= f(4)+ 12(4)+ 12 so it is sufficient to find to find f(4). And f(4)= f(2(2))= 4(f(2))+ 6 so we can get that from f(2). And f(2)= f(2(1))= 4(f(1))+ 6 which we can do because we know f(1).

spycrab, once you had told rcs how to do, it wasn't really necessary to do the calculation for him was it? Leave something for the OP to do- you lean mathematics by doing, not by watching someone else do mathematics!