## Plugging functions into fcn: If f(x + y) = f(x) + f(y)...

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Divine
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### Plugging functions into fcn: If f(x + y) = f(x) + f(y)...

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?

I don't understand what f(x + y) = f(x) + f(y) is.

Is it saying that if you plug in 2 numbers (x + y) into the function f, the value returned will be what would be returned by the same function if you plugged in each number separately ( f(x) and f(y) )?

I also don't understand what f(1) = 3 is saying. Is it stating that I'm plugging in 1 for x + y, so that (x + y) = 1, which then gets sent to the function for calculations?

What's more important to me is getting at the source of my confusion, so that I can solve this on my own.

nona.m.nona
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### Re: Plugging functions into fcn: If f(x + y) = f(x) + f(y)..

If f(x + y) = f(x) + f(y)...

I don't understand what f(x + y) = f(x) + f(y) is.
It is a function such that, if you plug a sum into the function, the function value of the sum is the sum of the functional values.
...and f(1) = 3,

find f(2), f(3), and f(4). Is f(x + y) = f(x) + f(y) for all functions?

Is it saying that if you plug in 2 numbers (x + y) into the function f, the value returned will be what would be returned by the same function if you plugged in each number separately ( f(x) and f(y) )?
Yes. In particular, since you have not been provided with any formal rule (that is, a formula) for the function, you must use the one value provided, being "f(1) = 3", to find other functional values by creating sums.

For instance, since 2 = 1 + 1 and since f(1 + 1) = f(1) + f(1), then you can find the value of f(2).