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Math Help - Composite function

  1. #1
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    Composite function

    I'm having trouble with these 2 composite function questions

    Find the requested composite function value

    1.f(x) = 7x + 8, g(x) = -2/x; find (g * f)(3)

    2.f(x) = x-6/10, g(x) = 10x + 6; find(g * f)(X)
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  2. #2
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    Quote Originally Posted by jay05 View Post
    I'm having trouble with these 2 composite function questions

    Find the requested composite function value

    1.f(x) = 7x + 8, g(x) = -2/x; find (g * f)(3)

    2.f(x) = x-6/10, g(x) = 10x + 6; find(g * f)(X)
    You say "composite functions" but use a standard multiplication symbol (*). Hopefully you mean composition, because that's what follows!
    -
    1. g(f(3)) can be found by first determining f(3), then finding "g of" this value.
    f(3) = 7(3) + 8 = 21 + 8 = 29. g(f(3)) = g(29) = -2/29.

    2. g(f(x)) = g((x - 6)/10) = ... can you take it from here?
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    Quote Originally Posted by jay05 View Post
    I'm having trouble with these 2 composite function questions

    Find the requested composite function value

    1.f(x) = 7x + 8, g(x) = -2/x; find (g * f)(3)

    2.f(x) = x-6/10, g(x) = 10x + 6; find(g * f)(X)
    What have you tried? Where are you stuck? Do you uderstand the notation (is it explained in your class notes or textbook?) Does * mean you're multiplying the two functions together ....?
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    Quote Originally Posted by TheChaz View Post
    You say "composite functions" but use a standard multiplication symbol (*). Hopefully you mean composition, because that's what follows!
    -
    1. g(f(3)) can be found by first determining f(3), then finding "g of" this value.
    f(3) = 7(3) + 8 = 21 + 8 = 29. g(f(3)) = g(29) = -2/29.

    2. g(f(x)) = g((x - 6)/10) = ... can you take it from here?
    the second x is kind of throwing me off, is x still equivalent to 1?
    if so those the equation = 1?
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  5. #5
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    Which question are we talking about?
    x is not equivalent (or equal) to 1 in either question. Where did you come up with that?
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    Quote Originally Posted by jay05 View Post
    the second x is kind of throwing me off, is x still equivalent to 1?
    if so those the equation = 1?
    Please address the questions I asked in post #3 if you need more help.
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  7. #7
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    the second question and i just thought that x = 1 like it did in previous algebra problems
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  8. #8
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    Quote Originally Posted by mr fantastic View Post
    What have you tried? Where are you stuck? Do you uderstand the notation (is it explained in your class notes or textbook?) Does * mean you're multiplying the two functions together ....?
    i understand the notation just having trouble with this and no * doesnt mean multiplication i just didnt know what to put in the middle
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  9. #9
    Super Member TheChaz's Avatar
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    Quote Originally Posted by jay05 View Post
    the second question and i just thought that x = 1 like it did in previous algebra problems
    This is bothering me. In which algebra problems did x = 1?

    In question (2), no x-values are specified, so we will end up with g(f(x)) = [some function of x].
    You can certainly determine the value of this function WHEN x = 1, but to say that x is equal to 1 is not correct.
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  10. #10
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    Quote Originally Posted by jay05 View Post
    I'm having trouble with these 2 composite function questions

    Find the requested composite function value

    1.f(x) = 7x + 8, g(x) = -2/x; find (g * f)(3)

    2.f(x) = x-6/10, g(x) = 10x + 6; find(g * f)(X)
    \displaystyle g(f(x)) = \frac{-2}{f(x)} = \frac{-2}{7x+8}. Substsitute x = 3 and get the value.

    Alternatively, f(3) = 29. Therefore g(f(3)) = g(29) = -2/29.

    Do the other one in the same way.
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