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The function f(x) has the property that f (x+y) = f(x)+f(y)+xy, for all positive integers x and y. If f(1) = 4, then what is the value of f(8)?

 Jan 6, 2021
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Answer: 60

 

Explanation:

We know f(1) = 4. Then we can find f(1+1) = f(2), because of the formula they give. Plugging in x=y=1 we get f(1+1)=f(1)+f(1)+1*1 --> f(2) = 4+4+1 --

f(2) = 9.

We can continue on until we get f(8). Letting x=y=2 we get f(2+2)=f(2)+f(2)+2*2 --> f(4) = 22. Finally, letting x=y=4 we get f(4+4)=f(4)+f(4)+4*4 --> f(8) = 60.

 

You are very welcome!

:P

 Jan 6, 2021

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