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Check This Please.

  1. Nov 18, 2004 #1
    For The Function F(x)= -x^2 +2 , Find F(3) And F(-4)

    This Is My Work:

    F(3) = -(3)^2 + 2
    3= -9 + 2
    3= -7
    (Then I Divided 3 From Both Sides)
    = -2.3

    F(-4)= -(-4)^2 + 2
    -4= -14
    (Then I Divided -4 From Both Sides)
    = 3.5

    Am I Doing This Right?...
     
  2. jcsd
  3. Nov 18, 2004 #2
    No.

    Your first step is right:
    [tex]F(3) = -(3)^2 + 2[/tex]

    This step is wrong:
    [tex]3= -9 + 2[/tex]

    It should be

    [tex]F(3) = -9+2[/tex]

    Same for the second.
     
  4. Nov 18, 2004 #3
    So I Just Need To Put The "F"?
     
  5. Nov 18, 2004 #4
    Well, they are asking you to solve for F(3), so you can just leave the left side as F(3). If they were asking you for F( :smile: ) then you would leave the left side as F( :smile: ).
     
  6. Nov 18, 2004 #5
    For The Function F(x)= -x^2 +2 , Find F(3) And F(-4)

    This Is My Work:

    F(3) = -(3)^2 + 2
    F(3)3= -9 + 2
    F(3)= -7
    (Then I Divided 3 From Both Sides)
    = -2.3

    F(-4)= -(-4)^2 + 2
    F(-4)= -14
    (Then I Divided -4 From Both Sides)
    F(-4)= 3.5
     
  7. Nov 18, 2004 #6
    Now Is That Right?
     
  8. Nov 18, 2004 #7
    No, why are you dividing by 3?

    If I asked you to solve for Bannana and I said that:
    [tex]Bannana = 2 + 7[/tex]

    You would say that,
    [tex]Bannana = 9[/tex]

    If I asked you to solve for Apple and said that

    [tex]Apple = 5+3-2[/tex]

    You would say that

    [tex]Apple = 6[/tex]

    Now if I asked you to solve for F( :smile: ) and said that

    [tex]F (x) = x + 3[/tex]

    You would say that

    [tex]F ([/tex] :smile: [tex])[/tex] = :smile: [tex]+ 3[/tex]

    Why would you divide by :smile: ?

    You solved for what I asked for, no need to go any further.
     
  9. Nov 18, 2004 #8
    So I Dont Need To Divide?
     
  10. Nov 19, 2004 #9

    Diane_

    User Avatar
    Homework Helper

    Think of it this way: if they had asked you to find 'y' in

    y = -x^2 + 2

    for x = 3, would you write

    3y = -3^2 + 2?

    Probably not. With a 'y' in there, it's very obvious that the 3 belongs only on the right-hand side, not the left hand side.

    Functional notation can be very confusing when you start, largely for the reasons you're encountering. You're making it harder than it needs to be, but don't feel bad about it because just about everyone does.

    Try this: if I write y = 3x + 2, how many variables do I have? Sure looks like two, doesn't it? But that's wrong - once I pick a value for x, I've automatically picked a value for y. So x is a variable - something that can take any value - but y really isn't. (Yes, we could view it the other way around, too - that y is the variable and x isn't. You'll get into that, but don't worry about it now.)

    The functional notation is intended to supress this confusion a bit. Instead of writing y, we write f(x), which means that x is the variable and there is another value, f(x), which depends on it. Pretty much any time you see f(x), you can replace it with a y and it will work just fine. Thinking of it that way may save you some grief in the long run.

    Hope that helps.
     
  11. Nov 19, 2004 #10

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    It's not just that you "don't need to divide". Why in the world would you think you SHOULD divide?

    "F(3) = -(3)^2 + 2
    F(3)3= -9 + 2
    F(3)= -7"
    The problem asked you to find F(3). Saying F(3)= something means you have found F(3). You don't need to go any farther.

    "(Then I Divided 3 From Both Sides)
    = -2.3"
    ?What happened to the left hand side? just "= -2.3" doesn't mean anything! WHAT is equal to -2.3? I emphasize that because I think it shows that you are just trying apply memorized operations rather than thinking about what you are doing. Remember what you were trying to find. I suspect you were thinking "divide" by 3 because you were interpreting "F(3)" as "F times 3". IF that were the case, you would still have "F=" but you were not asked to find that.

    One crucial point you should also understand: F(3) is NOT "F times 3". F(3) means exactly "what you get when you replace the x in the formula with 3". Once you have done that, and then done the arithmetic to simplify, you are done.
     
  12. Nov 20, 2004 #11
    Also, can't you see that there's something wrong with the line "3 = -7"??
     
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