SOLUTION: The function f(x) has the property that f(x+y)= f(x)+f(y)+2xy, for all positive integers x and y. If f(1)=5, then find the value of f(16).

Algebra ->  Functions -> SOLUTION: The function f(x) has the property that f(x+y)= f(x)+f(y)+2xy, for all positive integers x and y. If f(1)=5, then find the value of f(16).      Log On


   

Question 551941: The function f(x) has the property that f(x+y)= f(x)+f(y)+2xy, for all positive integers x and y. If f(1)=5, then find the value of f(16).
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

       f(x+y) = f(x) + f(y) + 2xy, f(1) = 5

f(2) = f(1+1) = f(1) + f(1) + 2(1)(1) = 5 + 5 + 2 = 12

f(4) = f(2+2) = f(2) + f(2) + 2(2)(2) = 12 + 12 + 8 = 32

f(8) = f(4+4) = f(4) + f(4) + 2(4)(4) = 32 + 32 + 32 = 96

f(16) = f(8+8) = f(8) + f(8) + 2(8)(8) = 96 + 96 + 128 = 320

That's the answer, f(16) = 320

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You weren't asked to find the general solution for

f(x) but I found it anyway.

It's f(x) = x(x + 4)

Edwin