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Need some help with Algebra II!

  1. Nov 8, 2009 #1
    I've got a question maybe you guys can answer.

    I'm in Algebra II and I was given a question that was worded like this:

    "If f(x) = x², then find f(x-y)-f(x)."

    Can someone help me? I don't really know how to solve it...

    -DukeGuy123
     
  2. jcsd
  3. Nov 8, 2009 #2

    lurflurf

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    Homework Helper

    f(x-y)-f(x)=(x-y)^2-x^2
    one would then likely be expected to expand and simplify
     
  4. Nov 8, 2009 #3
    That's not one of the valid answer choices...

    It's one of these four (it's multiple choice):

    A) 2x
    B) x²-2xy+y²
    C) -2xy+y²
    D) 2xy-y²

    Thanks for your help, but I would like to get an answer that is Correct and WITH WORK.

    I really don't know how to solve this.
     
  5. Nov 8, 2009 #4
    lurflurf, did you check the answer choices?

    Which answer choice would that be? And is there a more detailed way you can explain it, because I still don't get it.

    Can you show it like step-by-step or something?
     
  6. Nov 8, 2009 #5

    lurflurf

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    so f(x) = x² means that whenever you see f(*) were * is some expresion you replace it by *2
    so if you have
    f(x-y)-f(x)
    it gives
    (x-y)2-x2
    you should be able to expand (x-y)2 using foil or (a+b)2=a2+2 a b+y2
    then cancel
     
  7. Nov 8, 2009 #6
    yup! f(x) =x2 shows you how the function is affecting the variable

    if the variable inside the parentheses is something other than x, it is affected the same way that x would be as long as the function is still f, and not some other function.
     
  8. Nov 10, 2009 #7

    Mark44

    Staff: Mentor

    Anakin_k, it is against the policy in this forum to provide complete solutions to a poster's problems.
     
  9. Nov 10, 2009 #8

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Lurflurf Suggested you expand (x-y)2- x2. Have you done that yet?
     
  10. Dec 5, 2009 #9
    in case you didnt know (x-y)^2 is really (x-y)(x-y)
    with that knowledge you should be able to solve (x-y)(x-y) -x^2 just foil it all out!
    (x^2-xy-xy+y^2)-x^2
    combine like terms (x^2-2xy-y^2)-x^2
    the x'2s cancel oiut leaving you with -2xy-y^2
    factor out a -y -y(2x+y)

    if i didnt totally screw this up there's your answer.
     
  11. Dec 5, 2009 #10
    you dont multiply x-y times x squared. x-y IS x in this problem times the whole thing squared. thats what f(x)=x^2 is saying. its defining the function/ you did not substitute for x you just multiplied numbers by sx.
     
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