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Domain range intervals; please help if you can

  1. Jul 18, 2011 #1
    1. The problem statement, all variables and given/known data

    Hello. Can someon help me understand the difference between these two problems?
    #1: f(x)+3
    #2: f(x+3)

    The reason I want to know if becuase my question tells me to use the domain of f(x) as [4, 8] and the range as [2, 6]
    Then it wants to know the domain and range of both of those problems.

    My first question here is that I got [1, 5] as the domain, but I don't know if that pertains to the first or second problem. If it pertains to either of them, how do I do the other problem? Also, how do I find the range of both of these problems? Would it be [-1, 3] and again, for the first or second problem? I'm guessing both of my answers would go with the first, but yet again, I am not sure.[/quote]
    How did you "get" [1, 5] as domain and [-1, 3] as range without know which problem you were working on? In #1, you must calculate f(x) and then add 3. You are told that you can only calculate f(x) for x in [4, 8] so the domain should be obvious. If f(x) gives values between 2 and 6 what values are f(x)+ 3?

    If f(u) can be calculated for u in [4, 8] and u= x+ 3, what can x be? Which problem is that for? Well, the domain applies to the value inside parentheses in f() so which has x+3 inside the parentheses? Anything that is inside the parentheses- before you calculate f- affects the domain, anything outside affects the range.

    If your knowledge allows you, can you asist me in this problem? I keep looking at it and just can't seem to figure it out. Please help.

    Thanks in advance -Name_ask17
     
    Last edited by a moderator: Jul 19, 2011
  2. jcsd
  3. Jul 19, 2011 #2

    vela

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    You're given a function f which maps values in the domain [4, 8] to values in the range [2, 6]. That means any value you plug into f has to be between 4 and 8, and the value you get out of f will be somewhere between 2 and 6.

    For example, if you had f(x2), what you'd know is that x2 has to be between 4 and 8. If you have f(y+10), then y+10 has to be between 4 and 8, which means y has to be between -6 and -2. Whatever is between the parentheses has to be between 4 and 8.

    Now look at the first function. Let's call it g(x). You have g(x) = f(x)+3. What values of x can you plug into g so that what gets plugged into f is between 4 and 8? Those values make up the domain of g.

    Similarly, you have h(x) = f(x+3). What values of x can you plug into h so that what gets plugged into f is between 4 and 8?
     
  4. Jul 20, 2011 #3
    what is the difference between f(x) + 3 and f(x+3)?
     
  5. Jul 21, 2011 #4
    Let's assume f(x)= 2x. For f(x)+3, we plug in 2x for f(x) so it would be 2x+3. However, when it comes to f(x+3) you take what is inside the parenthesis and put it where the x is. So it would look like this f(x+3)=2(x+3). Hope this helps.
     
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