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Stupid Mistake?

  1. Jan 23, 2004 #1
    If f(x) = square root of x and g(x) = x + 1, then:

    1. What is f+g(x)?
    2. Domain of f+g(x)?
    3. What is f(g(x))?
    4. What is the domain of f(g(x))?

    I put:

    1. square root of x + x + 1
    2. x >= 0
    3. square root of x + 1
    4. All real numbers?

  2. jcsd
  3. Jan 23, 2004 #2
    Number 4 depends on whether you "allow" complex numbers or not...
  4. Jan 23, 2004 #3


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    Staff Emeritus
    Gold Member

    Just to make sure, do you mean
    sqrt(x) + x+1

    OK (as long as you are only talking about reals)

    Again, use parentheses.

    Nope. Example: x = -3.
  5. Jan 23, 2004 #4


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    Science Advisor

    In #2 you had already asserted that the domain of g+h (x)= √(x)+ x+1 is x>= 0 so you are talking about real valued functions of a real value (you can't take the square root of a negative number).

    In #4, then, f(g(x))= &radic(x+1), you must have x+1>= 0.
  6. Jan 23, 2004 #5
    Ug I hate it when I make mistakes like this! I knew how to do it and then when I'm under pressure I mess up everytime! Ack. So frustrating...lol... Oh well, just a quiz grade. Maybe I can make it up somehow...lol...
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