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Utterly simple

  1. Jun 21, 2007 #1
    I'm sorry for this, but what is the range and domain of the following function?

    y = 24 - 2x

    y has to be positive (y > 0) and x too (x > 0)

    How would you solve this? Do you just need a look and then be able to write it down? Or do you need to solve it with algebra?

    I've found that x can only be up to 12, or else y would be negative:

    y = 24 - 2x
    0 = 24 - 2x
    x = 12

    What is then the minimum of x?

    2x = 24 - y
    0 = 24 - y
    y = 24

    When y is 24, x is zero.

    This means:
    0 < x < 12

    With these values, y is always positive, we have solved the domain of the function.

    Is this correct?
     
    Last edited: Jun 21, 2007
  2. jcsd
  3. Jun 21, 2007 #2
    That's right.
     
  4. Jun 21, 2007 #3
    y > 0 implies 24 - 2x > 0 implies x < 12

    x > 0 implies 12 - 0.5y > 0 implies y < 24

    So: 0 < x < 12

    And: 0 < y < 24

    Good work. Also, don't apologise for wanting help.
     
  5. Jun 21, 2007 #4
    Thanks.


    But apparently the correct answer is:

    6 < x < 12 and
    0 < y < 12

    Is the key (answer) in the back of the book misprinted perhaps?
     
  6. Jun 21, 2007 #5
    yes completely wrong
     
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