I am no good in math so kindly help me!

if f(x+y) = f(x) + f(y), and f(1) = 3

Then find:

f(2)
f(3)
f(4)

I don't even know where to begin!

1/25/2009 3:12:11 AM

42

1/25/2009 3:56:12 AM

here's your hint:

2 = 1 + 1

1/25/2009 4:15:23 AM

You have to figure out the function first.

If f(1) = 3, then here are some obvious possibilites:

f(x) = x + 2
f(x) = 2x + 1
f(x) = 3x

See which of the functions above satisfies this condition:

f(x+y) = f(x) + f(y)

For example, let's try the 1st one: f(x) = x + 2

Left side: f(x+y) = x + y + 2

but

Right side: f(x) + f(y) = x+2 + y+2 = x + y + 4, which is not equal to the above (which was x + y + 2)

So the 1st one is out of the running. Try the other 2.

Once you know your function (whether 2nd or 3rd one, or another if those 2 don't work), then finding

f(2)
f(3)
f(4)

will be cake.

Post here when done, or if you need more help.

(I am assuming here you at least know how to find the outputs given any inputs, for any simple function... tell me my assumption is correct!)

1/25/2009 6:24:13 AM

^Thanks, man! I'll let you know once I try it out.

1/25/2009 9:49:11 AM

I guess my reply would have to be based on what math course this is for. But you should be able to recognize the solution very quickly without having to "guess and check".

The reason why:

You have to appreciate the meaning of f(x+y)=f(x)+f(y) .

This property has a special name, "additivity". It's a necessary condition for another property of functions we call, "linear maps" (or homomorphism in general).

So, we can immediately recognize that the function must be of the form f(x)=a*x
f(x)=a*x+b is NOT a linear map. (we call this affine)
Since, f(0)=f(0+0)=f(0)+f(0)= 2*f(0) , implies that f(0)=2f(0) , which is only true if f(0)=0.


So, once you see f(x+y)=f(x)+f(y) where x,y are real numbers you sould immediately think f(x)=a*x

So now you can solve for 'a', and get the solution quickly.

1/25/2009 10:37:37 AM

6
9
12

1/25/2009 12:24:13 PM

i feel like i should know how to do this, then again i don't care

I'm Big Business and i approved this message.

1/25/2009 2:28:50 PM

i wish this were in Chit Chat

i'd love to make a "Meth problem help!" parody

1/25/2009 2:55:58 PM

^^yupp thats right

1/25/2009 4:05:47 PM

clalias, i know what you said. i have a master's degree in the mathematical sciences after all.

BUT, it is obvious the OP is taking a very elementary course, and i doubt they have talked about linear mappings, or any of the other stuff you said.

1/25/2009 4:43:04 PM

Quote :

"(or homomorphism in general)"

[no homo]

1/25/2009 6:14:59 PM

^^yeah I understand. I was just trying to give some meaning behind the problem. But your response was probably more appropriate. Well, maybe he learned something from my post anyway.

1/25/2009 6:54:17 PM

Quote :

"i feel like i should know how to do this, then again i don't care"

Quote :

"Well, maybe he joe_schmoe learned something from my post anyway."

1/26/2009 4:42:56 PM