SOLUTION: If f(x+y)=f(x)+f(y) and f(1)=17, find f(2), f(3), and f(4). Is f(x+y)=f(x)+f(y) for all functions? f(2)= f(3)= f(4)=

Algebra ->  Functions -> SOLUTION: If f(x+y)=f(x)+f(y) and f(1)=17, find f(2), f(3), and f(4). Is f(x+y)=f(x)+f(y) for all functions? f(2)= f(3)= f(4)=      Log On


   

Question 1160164: If f(x+y)=f(x)+f(y) and f(1)=17, find f(2), f(3), and f(4). Is f(x+y)=f(x)+f(y) for all functions?
f(2)=
f(3)=
f(4)=
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.

then  f(2) = f(1 + 1) = f(1) + f(1) = 17 + 17 = 34.     ANSWER


      f(3) = f(1 + 2) = f(1) + f(2) = 17 + 34 = 51.     ANSWER


      f(4) = f(2 + 2) = f(2) + f(2) = and you continue from this point.

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For the last question, the answer is "NO".

As an counterexample, consider f(x) = x^2.


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