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Domain and Range of functions

  1. Sep 2, 2010 #1
    Could someone please explain to me what the range and domain of a function is and how to find them? I just don't understand what they mean
    Thank You
     
  2. jcsd
  3. Sep 2, 2010 #2

    Mark44

    Staff: Mentor

    The domain of a function is the set of all valid inputs to the function. The range is the set of all possible outputs.

    For example, if f(x) = 1/x2, the domain is all real numbers except 0. The range is all real numbers greater than 0.

    D = {x in R | x [itex]\neq[/itex] 0}
    R = {y in R | y > 0}
     
  4. Sep 2, 2010 #3
    Domain is all the possible values that X could be
    Range is all the possible values that Y could be

    example: determine the domain and range of y= x^2

    when u sketched the graph, you can see x could be anything, it keeps going forever there for D( -infinity, +infinity)

    for y, however, you can see y never goes below x axis, the maximum value for y is just 0
    therefore (0, +infinity), because y goes up forever.
     
  5. Sep 2, 2010 #4
    But domain and range cant share a common number Can they?
     
  6. Sep 2, 2010 #5

    Mark44

    Staff: Mentor

    Sure, why not?
     
  7. Sep 3, 2010 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    They don't have to but they certainly can.

    For example, the domain and range of f(x)= 2x+ 1 are both "all real numbers". Given any real number, I can certainly multiply it by 2 and then add 1- the domain is all real numbers. On the other hand, for any real number x, f(x)= 2x+ 1= y if 2x= y- 1 or x= (y- 1)/2 which is a real number. Since I can get any real number as a result of f(x) the range is all real numbers.
     
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