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Math Help - Determine the following please:

  1. #1
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    Determine the following please:

    I need to check my answers and don't know the solutions

    Let f(x) = 1/x and g(x) = -2x + 5. Determine the following:

    a.) f ( g (1) ) = _____________________________
    b.) g ( f (1) ) = ____________________________
    c.) f ( g (x) ) = ____________________________
    d.) g ( f (x) ) = ____________________________
    e.) f (2)g(2) = _____________________________
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  2. #2
    ixo
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    I'm not going to work all your problems for you but this is how you do it:
    think of f(g(x)) = 1/(-2x + 5) and g(f(x)) = -2(1/x) + 5.

    Example:

    If f(x) = 2x and g(x) = 3x and h(x) = 4x
    then f(g(x)) = 2( 3x ) and f(h(x)) = 2( 4x)
    similarly g(f(x)) = 3( 2x ) and g(h(x)) = 3( 4x )
    as well as
    f(x)g(x) = (2x)(3x)

    Whatever is inside the parenthesis is what you place as x for the equation. If f(x) = 2x and they ask you to evaluate f(2) then its just simply 2(2) and g(5) = 3(5).

    Hope this helps
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  3. #3
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    Thanks, that helps.

    So for a. I got 1/3

    for b. I get 3

    and for e. I get 4 1/2.

    Thanks for any feedback.
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  4. #4
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    Quote Originally Posted by Humbled_by_math View Post
    I need to check my answers and don't know the solutions

    Let f(x) = 1/x and g(x) = -2x + 5. Determine the following:

    a.) f ( g (1) ) = _____________________________
    b.) g ( f (1) ) = ____________________________
    c.) f ( g (x) ) = ____________________________
    d.) g ( f (x) ) = ____________________________
    e.) f (2)g(2) = _____________________________
    a) and b) are right. I think you got e) wrong:

    e) 1/2(-4 + 5) = -2 + 2 1/2 = 1/2

    But I'm sure you can see why.
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  5. #5
    ixo
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    f(2)g(2) = (1/(2))(-2(2) + 5)
    = 1/2(-2(2)+5)
    = 1/2(-4+5)
    = 1/2(1)

    = 1/2

    Last edited by ixo; February 7th 2009 at 11:58 AM.
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