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Math Help - Functions

  1. #1
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    Functions

    Can someone please help me again?


    Given that f(x)=3x^2-3\ \mbox{and}\ g(x)=\sqrt{x-2}

    evaluate

    fg (x)


    I am a bit confused on how to multiply these two functions.
    Am I allowed to times each of the terms under the square root sign separately(probably not)?



    How do I perform this operation then?


    Thank you!
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  2. #2
    Senior Member tukeywilliams's Avatar
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    Its probably asking for the composition of  f and  g .  fg(x) is another way of writing  f \circ g or  f(g(x)) .

    So  f \circ g = 3(\sqrt{x-2})^2 - 3 = 3x-9 .
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  3. #3
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    Thank you!


    I don't really know if this is asking for composite functions(since we still have not gone through them), but our teacher told us to substitute the function of f(x) in the place of f and then times the two functions.


    For example

    if we had (f+x) (6) then it would have been 3x^2-3+\sqrt{x-2} substituing 6 in place of x.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Coach View Post
    Thank you!


    I don't really know if this is asking for composite functions(since we still have not gone through them), but our teacher told us to substitute the function of f(x) in the place of f and then times the two functions.


    For example

    if we had (f+x) (6) then it would have been 3x^2-3+\sqrt{x-2} substituing 6 in place of x.
    that notation makes no sense. i think you meant f(x + 6), in which case, that would be 3(x + 6)^2 - 3 ........and you would simplify that
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  5. #5
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    Ok.

    I think you may be right, but that is exactly what my homework says.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Coach View Post
    Ok.

    I think you may be right, but that is exactly what my homework says.
    it's probably a typo then.
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Coach View Post
    Can someone please help me again?


    Given that f(x)=3x^2-3\ \mbox{and}\ g(x)=\sqrt{x-2}

    evaluate

    fg (x)


    I am a bit confused on how to multiply these two functions.
    Am I allowed to times each of the terms under the square root sign separately(probably not)?



    How do I perform this operation then?


    Thank you!
    Quote Originally Posted by tukeywilliams View Post
    Its probably asking for the composition of  f and  g .  fg(x) is another way of writing  f \circ g or  f(g(x)) .

    So  f \circ g = 3(\sqrt{x-2})^2 - 3 = 3x-9 .
    tukeywilliams is probably right, but if you see the notation
    (fg)(x)
    it means simply to multiply f(x) and g(x).

    Similarly:
    (f/g)(x) = f(x)/g(x)
    (f + g)(x) = f(x) + g(x)
    (f - g)(x) = f(x) - g(x)

    -Dan
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