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Application in Set Theory

  1. Oct 25, 2011 #1
    Polynomial Function.

    1. The problem statement, all variables and given/known data

    f:ℝ→ℝ
    x→x^2+x+2

    2. Relevant equations

    Prove that: f(ℝ)=[7/4,+∞[

    3. The attempt at a solution

    Well I don't know how answer this, so can someone give me a clue on how to start it off?
     
    Last edited: Oct 25, 2011
  2. jcsd
  3. Oct 25, 2011 #2
    What is the minimum value of x2+x+1?
     
  4. Oct 25, 2011 #3
    the minimum value for x^2+x+1 is obviously 1
     
  5. Oct 25, 2011 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If x=-1/2, [itex]x^2+ x+ 1= 1/4- 1/2+ 1= 3/4[/itex]. Try thinking before reacting!
     
  6. Oct 26, 2011 #5
    Yea thanks for the tip i already tried it out yesterday and i figured it out.

    Once i stated that x=-1/2 then i get x^+x+2=7/4
     
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