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Range of a function, very simple & basic question

  1. Dec 30, 2009 #1
    Just go through the following problem

    Question 1:find the range of the following function
    f(x)=3x2+4 for -4≤x≤3

    Answer:
    rewriting -4≤x≤3
    step1. 0≤x2≤16
    step2. multiply 3 for the entire step 1.
    step4. add 4 for the entire step1.
    step5. 4≤f(x)≤52

    so the above problem i have understood

    now how do i solve the following problem using the same method as above, because the following problem is a bit different from the first one, and i get a reverse answer

    Question 2: find the range of the following function
    f(x)=9-2x2 for -3≤x≤3

    rewriting -3≤x≤3
    step 1. 0≤x2≤9 now is this step correct?, i dont think so.
    step 2. ????????
    step 3. ????????
    step 4. ????????

    plz note: i cannot find the range directly because each step carries marks
     
    Last edited by a moderator: Dec 30, 2009
  2. jcsd
  3. Dec 30, 2009 #2
    The step is correct. .

    if you square x<=3 that will give you (x^2 <=9) or (x<0)
    if you square x>=-3 that will give you ((x^2 <= 9) or (x>0))

    if both are true you just get (x^2 <= 9)
     
  4. Dec 30, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, it is correct. Why would you not think so?

    Multiplying each part of the inequality by negative 2 reverses the inequality:
    [itex]-18\le x^2\le 0[/itex]
    Since you say you got a "reverse answer" that may have been your mistake.

    Add 9 to each part.

    Write down your answer!

     
  5. Dec 30, 2009 #4
    @HallsofIvy

    oh thanks a lot, that helped me
     
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