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Question 1139678: If f(x + y) = f(x) + f(y) and f(1) = 3, Find f(2), f(3), and f(4). Is f(x + y) = f(x) + f(y) for all
functions?
Answer by ikleyn(52847)   (Show Source):
You can put this solution on YOUR website! .
Since f(x+y) = f(x) + f(y) ( ! GIVEN ! ), we have
f(2) = f(1+1) = f(1) + f(1) = 3 + 3 = 6;
f(3) = f(2+1) = f(2) + f(1) = 6 + 3 = 9;
f(4) = f(3+1) = f(3) + f(1) = 9 + 3 = 12.
Answered, explained, solved and completed.
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I got your comment about the second question in the post.
The answer is very simple.
From my previyus calculations, you see the the function f(x) with given properties must be linear.
But not every function is linear.
For example, quadratic functions are not linear.
All polynomial functions are not linear.
All square root functions of the form f(x) =  are not linear.
All exponential functions are not linear.
As well as millions other functions.
Next time, when you want to communicate with me in this way, please refer to the ID number of the problem.
In this case the ID number is 1139678.
Otherwise, I will not know to whom to answer - it is how this forum works !
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