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Math Help - functions involving radical

  1. #1
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    functions involving radical

    what if the radical is in the denominator?
    y=\frac{2}{x^2+8x+10}

    the domain is \{x|x^2+8x+10\ge 0\}

    so the domain is x^2+8x+10\ge0

    \frac{4ac-b^2}{4a}

    \frac{40-64}{4}

    -4

    x\ge-4??

    range: ??

    is this correct?
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  2. #2
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    First check where  x^2+8x+10=0
    Solution is x= -6.5 and -1.6

    This means as domain is x\ge0 so the equation      x^2+8x+10 is always positive.

    This means if x=0,y=  \frac{2}{0^2+8(0)+10} = \frac{1}{5}

    As x^2+8x+10 always increases when increases, So the value of this function  \frac{2}{x^2+8x+10} decreases.
    Hence max. value this function can have is \frac{1}{5} and the graph of this function tends to zero, when x increases but can never be equal to zero.

    Range : \frac{1}{5}\ge y>0
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  3. #3
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    how did you get and ?
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  4. #4
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    Talking

    Quote Originally Posted by princess_21 View Post
    how did you get x = -6.5 and x = -1.6?
    The poster solved the quadratic equation.

    You can, for instance, use the Quadratic Formula for this....
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  5. #5
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    Quote Originally Posted by princess_21 View Post
    how did you get and ?
    I have used this formula to solve x^2+8x+10=0 :

    \frac{-b\pm\sqrt{b^2-4ac}}{2a}

    Where standard equation is this one: ax^2+bx+c
    a=1, b=8, c=10

    Plug in the values to solve the equation.
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