Question

Functions

Answer 1

f(3x) = x + f(3x-3)
f(3) =1
Find f(300)

Answer 2

3x = 3 when x=1

f(3) = 1 + f(0)

do we have to work this with repetition maybe? a little more context might be useful

Answer 3

when x=100, f(300) = 100 + f(97) but im not sure that useful to us

Answer 4

I did that

Answer 5

f(300) = 100 + 99 + 96 + 97 + 96 + ...

Answer 6

say u = 3x, x = 1/3 u

f(u) = 1/3 u + f(u-3)

not sure how that would be helpful either

Answer 7

But it does not make a series or something

Answer 8

are the functions linear?

f(ka+cb) = k f(a) + c f(b)

Answer 9

that is just another form ,

Answer 10

I have not studied functions formally so i am able to get u

Answer 11

consider this like a sequence or series is what im thiking

Answer 12

x = 0,1,2,3,4 ,5 ,...
f(3x) = 0,3,6,9,12,15,...
f(3x-3) = -3,0,3,6,9,12,15,...

Answer 13

somethings brewing in there just not sure what it is

Answer 14

f(3n) = n(n+1)/2 will do i think

Answer 15

f(3x) = x + f(3x-3)
f(3) =1

If we construct another sequence by picking every third term from above sequence, we get :
g(t) = t + f(t-1)
g(1) = 1

which is clearly a recurrence relation sum of first t terms, so the solution is
g(t) = t(t+1)/2

Answer 16

plugging in t = 100 gives f(300)

g(100) = 100(100+1)/2 = 50*101 = 5050

Answer 17

sounds reasonable to me :)