A function equation

[Kalen12]

While practicing math I stumbled upon an equation that goes like this:

Solve for f(3) if 2f(x) + f(3-x) = x

This is what I managed to do with it:

2f(3) + f(0) = 3
for f(0) 2f(0) +f(3) = 0

I have the correct answer which is 2, but I don't know how to get to it. I don't understand how to get to that answer. If someone could help me with this it would be great, thanks in advance.

 

[Harry_the_cat]

Let f(3) =a and f(0) = b
Then you have 2 simultaneous equations:
2a + b = 3 and
2b + a =0.
Can you go from there?

 

[Kalen12]

Let f(3) =a and f(0) = b
Then you have 2 simultaneous equations:
2a + b = 3 and
2b + a =0.
Can you go from there?

I don't know how didn't that come to mind..
Thanks a lot.
It's quite simple now.

2a+b=3
a+2b=0/(-2)
2a+b=3
-2a-4b=0
-3b=3
b=-1
a= 2

So this means that f(3)= 2 and that f(0)= -1 ,right?

 

[Deleted member 4993]

I don't know how didn't that come to mind..
Thanks a lot.
It's quite simple now.

2a+b=3
a+2b=0/(-2)
2a+b=3
-2a-4b=0
-3b=3
b=-1
a= 2

So this means that f(3)= 2 and that f(0)= -1 ,right?

You can confirm your answer yourself.

2a + b = 3 and
2b + a =0.

Are both of those equations satisfied by

b=-1
a= 2

Looks to me - Yes. Thus you are most probably correct.

 

[Kalen12]

Okay, thanks a lot.

 

[Otis]

… a + 2b = 0/(-2) …

… -2a - 4b = 0 …

Hi Kalen. That is a typo, yes? We multiply both sides by -2, to get the next equation above.

(-2)(a + 2b) = (-2)(0)

-2a - 4b = 0

?

 

[Kalen12]

Hi Kalen. That is a typo, yes? We multiply both sides by -2, to get the next equation above.

(-2)(a + 2b) = (-2)(0)

-2a - 4b = 0

?

No, it isn't. Take a better look, it's a system of equations so the first one is not multiplied I just multiplied the second one. Got the correct results too by solving it, so yeah take a better look it should be all fine.
Best regards

 

[Otis]

No, it isn't [a typo] Take a better look … the first [equation] is not multiplied I just multiplied the second one … so yeah take a better look …

Yes, Kalen, you multiplied both sides of the second equation by -2. (I didn't comment about the first equation.)

But, multiplying each side by -2 is not what you typed. Your typing shows division by -2, and you showed the division on only one side.

Take a better look.

\(\;\)

 

[Steven G]

Kalen, on this site we really like to see everything written correctly. I suspect that when you wrote /(-2) you meant that you plan on multiplying both sides by -2. However you did not write that (take a better look). I assure you that I would have taken points off on an exam if that right hand side was other than 0. That is 0 does equal 0/-2 so you were lucky. But if the rhs was 7 and you wrote 7/-2 I would have written -2 points

 

[Harry_the_cat]

Kalen its your use of the symbol / that is incorrect.
/ means division. But you've used it to mean something else like "multiply both sides of this equation by -2". What you have done is correct, it is the language (symbolism) that you have used incorrectly.