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Math Help - finding the range for the functions

  1. #1
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    finding the range for the functions

    im stuck on these last two questions can anyone please help

    find the range of these functions for XER

    1) 1 / (x^2 + 2)

    2)1 / (x^2 + 4x +5)

    thanks
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  2. #2
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    Quote Originally Posted by mike--1988 View Post
    im stuck on these last two questions can anyone please help

    find the range of these functions for XER

    1) 1 / (x^2 + 2)

    2)1 / (x^2 + 4x +5)

    thanks
    HI

    (1) Let y=\frac{1}{x^2+2}

    yx^2+2y-1=0

    b^2-4ac\geq 0 since x\in R

    -4y(2y-1)\geq 0

    4y(2y-1)\leq 0

    so y\in [0,\frac{1}{2}]

    The other one can be solved using this method too .
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  3. #3
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    i dont quite understand the method here
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  4. #4
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    Quote Originally Posted by mike--1988 View Post
    i dont quite understand the method here
    the idea here is to find the range of y which is also the range of the function . When given an equation ,knowing that its roots are real , do you know how to find its discriminant ?
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  5. #5
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    ive looked over it again and i understand it now , thank you
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