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Domain of the function

  1. Oct 8, 2009 #1
    Find the range of the equation.



    f(x)=x²+4


    Things I know for sure:
    x²>=0

    We are brushing up on functions and interval notation in my calc class, and I can't remember how to do this in interval notation. If x is a number being squared it has to be positive or zero. So at the minimum the answer is going to be:
    f(x)=0+3

    f(x)=3

    So the interval notation would be what? Quick little explanation would help as well. Thanks.
     
    Last edited: Oct 8, 2009
  2. jcsd
  3. Oct 8, 2009 #2

    Office_Shredder

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    The domain of the function is all the possible inputs for your function. You seem to be looking at the range
     
  4. Oct 8, 2009 #3
    You're right, that's what I meant. Good call. But what about interval notation?
     
  5. Oct 8, 2009 #4
    Careful, I think you're confusing domain and range.

    The range is [4,inf), the domain is (-inf,inf).

    Basically the domain is a set of numbers that x can satisfy. For example g(x) = 1/x the domain is (-inf,0)U(0,inf) because g(x) is not defined at x=0.

    The range is a set of numbers that your function can have as a value for a given domain of values. For example h(x) = x^2 has a range of [0,inf) since the minimum value of h(x) is 0 and the function will extend to infinity.

    If a number is exclusive we use parenthesis, and if a number is inclusive we use brackets. So in the case of the domain of g(x) = 1/x, x cannot equal zero but it can approach the value of 0 so 0 is exclusive. Negative and positive infinity are always exclusive since they are not actual values. Therefore (-inf,0) is in parenthesis on both sides. But that's not the entire domain! We can have x>0 so we need to include that too. We write include (or union) with a capitol U so the answer is (-inf,0)U(0,inf).
     
    Last edited: Oct 8, 2009
  6. Oct 8, 2009 #5
    Great, that helps a lot. Thanks.
     
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