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Math Help - function

  1. #1
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    function

    Given two functions , f(x)=x^2+3 , where x is real , g(x)=|x|-5 , x is real , find gf(x).

    i found gf(x)=x^2-2

    is it true that the range of gf(x) is the same as the range of g(x) ? If so,

    the range of g(x) is [-5 , infinity) and the range of gf(x) is [-2 , infinity)

    why arent they the same ?
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  2. #2
    Senior Member Stroodle's Avatar
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    g(f(x))=\left | x^2+3 \right |-5
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  3. #3
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    Quote Originally Posted by thereddevils View Post
    Given two functions , f(x)=x^2+3 , where x is real , g(x)=|x|-5 , x is real , find gf(x).

    i found gf(x)=x^2-2

    is it true that the range of gf(x) is the same as the range of g(x) ? If so,

    the range of g(x) is [-5 , infinity) and the range of gf(x) is [-2 , infinity)

    why arent they the same ?
    It is NOT true in general that the range of g(f(x)) is equal to the range of g(x) so your results are hardly surprising.

    Quote Originally Posted by Stroodle View Post
    g(f(x))=\left | x^2+3 \right |-5
    Irrelevant since |x^2 + 3| = x^2 + 3 because x^2 + 3 is always positive.
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  4. #4
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    Quote Originally Posted by Stroodle View Post
    g(f(x))=\left | x^2+3 \right |-5
    hello strodle , thanks for replying but thats not my question . I would like to know whether the range of g(x) the same as the range of gf(x) ? If i draw the set diagrams with the arrows , i found them to be the same . Take a look at the diagram i attached . gf(x) and g(x) both arrive at the same set

    Anyways , gf(x) could be further simplified knowing that x^2+3 is positive .
    Attached Thumbnails Attached Thumbnails function-function.bmp  
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  5. #5
    Senior Member Stroodle's Avatar
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    Oh yeah, sorry. I misunderstood the question...
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