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Math Help - Sum, product and difference of function question

  1. #1
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    Sum, product and difference of function question

    I am having trouble with the following question.
    Two functions are defined as f(x)=-x^2  g(x)=sqrt{x}

    a) Find the smallest possible value of a given that the domain of the function h, where h(x)=(f+g)(x), is a is less than or equal to x and 2 is greater than or equal to x
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  2. #2
    Senior Member Sambit's Avatar
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    Quote Originally Posted by johnsy123 View Post
    Find the smallest possible value of a given that....
    Means what???
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  3. #3
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    I presume that you mean you want to find a so that a\le x\le 2 is the domain of h(x)= -x^2+ \sqrt{x}.

    Okay, what kinds of numbers would NOT give a value for -x^2+ \sqrt{x}?

    (Hint: you can ignore the x^2 term.)
    Last edited by HallsofIvy; February 23rd 2011 at 04:46 AM.
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  4. #4
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    Hello, johnsy123!

    Very clumsy and misleading wording!

    WHO wrote this question?
    . . Public flogging may be appropriate punishment.


    \text{Two functions are de{f}ined as: }\:f(x)=\text{-}x^2,\;g(x)=\sqrt{x}

    \text{Let }h(x) \,=\,(f+g)(x)

    \text{(a) Given that the domain of }h(x)\text{ is: }\:a \le x \le 2

    . . . . \text{find the smallest possible value of }a.

    Now that I understand the problem, it's too easy.


    We have: . h(x) \:=\:-x^2 + \sqrt{x}

    We see that \,x must be nonnegative.

    So, the domain is: . 0 \le x \le 2

    . . Therefore: . a = 0. . .Duh!

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  5. #5
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    How does a=0? why can't a= 1 or a=2?

    All negative numbers.

    And i have one more question, if thats okay.
    How would i find the range of that function?
    Last edited by mr fantastic; February 23rd 2011 at 04:56 AM. Reason: Merged posts.
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  6. #6
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    Quote Originally Posted by johnsy123 View Post
    How does a=0? why can't a= 1 or a=2?
    Because they are not smallest. And your problem asked you to "Find the smallest possible value of a".

    Quote Originally Posted by johnsy123 View Post
    All negative numbers.
    ??? What is this in response to? There are no negative numbers in the domain of square root if that is what you meant.

    Quote Originally Posted by johnsy123 View Post
    And i have one more question, if thats okay.
    How would i find the range of that function?
    Your function is f(x)= -x^2+ \sqrt{x} with 0\le x\le 2. It is easy to see that the smallest value of f(x) occurs when x= 2: f(2)= -4+ \sqrt{2} but the maximum value is harder. I recommend graphing the function between x= 0 and x= 2.
    Last edited by mr fantastic; February 23rd 2011 at 04:56 AM. Reason: Merged posts.
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