Functions

[Lee]

I am totally confused!!! For which of the following is f(a+b) = f(a)+f(b) for all positive numbers a+b?

The answer is f(x) = -3x


How do I come up with this answer??

Thanks in advance

[JonathanSchneider]

You can try it out with some real numbers. Try something small, like 3 and 5.

Plugging in (3+5) = plugging in 8 ----> result = -24

Plugging in 3 ----> result is -9
Plugging in 5 ----> result is -15
Add together -9 and -15 ----> result is -24. A match.

Better yet if you can approach this with an understanding of the number properties (or in this case arithmetic properties) involved. We are really being asked: which arithmetic process carries across addition when that addition is inside parentheses the same as when the addition is not inside parentheses? Multiplication does that.