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Easy Question

  1. Sep 13, 2006 #1
    Let f = {(-4.4),(-2,4),(1,3),(3,5),(4,6)}

    and g = {(-4,2),(-2,1),(0,2),(1,2),(2,2),(4,4)}

    Determine a)f + g
     
  2. jcsd
  3. Sep 13, 2006 #2

    chroot

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    What are your thoughts?

    - Warren
     
  4. Sep 13, 2006 #3
    honestly i'm confused...
    f(x)=-4x+4? etc....?
    It's not (-4,4)+(-4,2)
     
  5. Sep 13, 2006 #4

    chroot

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    What's the value of the function f at, say, -4?

    What's the value of the function g with the same input, -4?

    What's the sum of the values of the two functions, given the same input, -4?

    - Warren
     
  6. Sep 13, 2006 #5
    wouldn't it be (-8,6)
     
  7. Sep 13, 2006 #6

    chroot

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    No, the input -- the value on the left -- is still -4. The summed outputs of both functions, however, is indeed 4+2 = 6.

    You have thus found the first input-output pair of the sum of f+g, (-4, 6).

    In english, this means if you plug -4 into f(x) + g(x), you get f(-4) + g(-4) = 4+2 = 6.

    - Warren
     
  8. Sep 13, 2006 #7
    Is this adding two sets f and g or is this adding function f to function g? The way it's written I assumed it was creating a union of two sets.
     
  9. Sep 13, 2006 #8
    but whats the equation of f(x)=?
    It looks like you set x to zero

    why does left side -4 stay the same .....?
     
    Last edited: Sep 13, 2006
  10. Sep 13, 2006 #9

    chroot

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    daveb,

    You have a good point. This question is a little ambiguous. However, simply taking the union of two sets means that the resulting function f+g is multivalued at -4, for example, which means it's no longer a function.

    Adding the outputs of the two functions is also a little tricky, since f is defined at 3, for example, while g is not. The sum of the two functions at 3 is thus also undefined, since anything + undefined = undefined.

    The first set is f(x), for x values -4, -2, 1, 3, and 4.

    The second set is g(x), for x values -4, -2, 0, 1, 2, and 4.

    The only input values common to both functions are -4, -2, 1, and 4. These are thus the input values acceptable to the function f+g. All other possible input values have no defined output.

    The output values of f+g are each the sum of the outputs of f and g at the same point. Thus, if you plug in -4 to f+g, you get f(-4) + g(-4) = 4+2 = 6.

    - Warren
     
  11. Sep 13, 2006 #10
    oh so ur saying that when adding them you have to have the same x value
     
  12. Sep 13, 2006 #11

    chroot

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    Yes. When you give the function f the input -4, it produces the output 4. When you give the function g the input -4, it produces the output 2.

    When you give the sum of the two functions, f+g, the input -4, the result is the sum of the outputs, 4+2 = 6.

    Thus, one member of the resulting set for f+g should be (-4, 6).

    - Warren
     
  13. Sep 13, 2006 #12
    thank you my friend
     
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