pleeaaseee help

[z51]

. Consider the function f : Z → Z with the following properties:
i. f(1) = 0
ii. f(m + n) = f(m) + f(n) + 3(4mn − 1)
Then, the value f(9) is equal to:
Α. 408 Β. 409 c. 410 d. 411 Ε. 412

it sais that the answer is A but i have no idea how to find it.

omg i just solved it...... thanks alot!!

 

[Deleted member 4993]

. Consider the function f : Z → Z with the following properties:
i. f(1) = 0
ii. f(m + n) = f(m) + f(n) + 3(4mn − 1)
Then, the value f(9) is equal to:
Α. 408 Β. 409 c. 410 d. 411 Ε. 412

If I were to solve this problem - I would calculate:

f(2) = f(1+1) = ?

 

[HallsofIvy]

. Consider the function f : Z → Z with the following properties:
i. f(1) = 0
ii. f(m + n) = f(m) + f(n) + 3(4mn − 1)
Then, the value f(9) is equal to:
Α. 408 Β. 409 c. 410 d. 411 Ε. 412

it sais that the answer is A but i have no idea how to find it.

omg i just solved it...... thanks alot!!

Since you have solved this,
f(2)= f(1+ 1)= f(1)+ f(1)+ 3(4(1)(1)- 1)= 0+ 0+ 3(3)= 9
f(4)= f(2+ 2)= f(2)+ f(2)+ 3(4(2)(2)- 1)= 9+ 9+ 3(15)= 18+ 45= 63
f(8)= f(4+ 4)= f(4)+ f(4)+ 3(4(4)(4)- 1)= 63+ 63+ 3(63)= 5(63)= 315

f(9)= f(8+ 1)= f(8)+ f(1)+ 3(4(8)(1)- 1)= 315+ 0+ 3(31)= 315+ 93= 408.

 

[z51]

Since you have solved this,
f(2)= f(1+ 1)= f(1)+ f(1)+ 3(4(1)(1)- 1)= 0+ 0+ 3(3)= 9
f(4)= f(2+ 2)= f(2)+ f(2)+ 3(4(2)(2)- 1)= 9+ 9+ 3(15)= 18+ 45= 63
f(8)= f(4+ 4)= f(4)+ f(4)+ 3(4(4)(4)- 1)= 63+ 63+ 3(63)= 5(63)= 315

f(9)= f(8+ 1)= f(8)+ f(1)+ 3(4(8)(1)- 1)= 315+ 0+ 3(31)= 315+ 93= 408.

thanks!! youre great!