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Math Help - Functions to find Values

  1. #1
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    Functions to find Values

    I've tried every way I could think of, but I can't seem to get it right. How do you find the value of g(f(a)) when g(x)= x^2-2 and f(x)=-2x+7 p.s. I know the answer is 4a^2-28a+47..but I want to work through the problem.
    Last edited by Yommz; January 16th 2013 at 06:53 PM.
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  2. #2
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    Re: Functions to find Values

    You offer us g(x) and h(x). Did you mean f(x) instead of h(x), or vice versa?
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  3. #3
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    Re: Functions to find Values

    I fixed it.
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    Re: Functions to find Values

    g(x) = x^2 2
    f(x) = -2x+7
    First substitute x as a
    f(a) = -2a +7
    then
    g(f(a)) = g(-2a+7)
    = (-2a+7)^2 - 2
    = 4a^2 - 28a + 47
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  5. #5
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    Re: Functions to find Values

    Quote Originally Posted by Mathivadhana99 View Post
    g(x) = x^2 2
    f(x) = -2x+7
    First substitute x as a
    f(a) = -2a +7
    then
    g(f(a)) = g(-2a+7)
    = (-2a+7)^2 - 2
    = 4a^2 - 28a + 47
    Excellent!
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  6. #6
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    Re: Functions to find Values

    What formula did you use to get 4a^ 2-28a+4 from (-2a+7)^ 2-2?
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  7. #7
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    Re: Functions to find Values

    (-2a+7)^2 - 2 = (-2a+7)(-2a+7) - 2 = (-2a)(-2a + 7) + (7)(-2a+7) - 2

    = (-2a)(-2a) + (-2a)(7) + (7)(-2a) + (7)(7) - 2

     = 4a^2 - 14a - 14a + 49 - 2 = 4a^2 - 28a + 47
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  8. #8
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    Re: Functions to find Values

    you apply (a+b)^2 formula
    (a+b)^2 = a^2 + 2ab + b^2

    (-2a+7)^2 -2 = (-2a)^2 + 2(-2a)(7) + (7)^2 - 2
    = 4a^2 - 28a + 49 - 2
    = 4a^2 - 28a +47
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  9. #9
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    Re: Functions to find Values

    the formula Mathivadhana99 used above is the same one i used:

    (a+b)^2 = (a+b)(a+b) = (a)(a+b) + (b)(a+b)

     = (a)(a) + (a)(b) + (b)(a) + (b)(b).

    since multiplication of real numbers is commutative:

    (b)(a) = ba = ab = (a)(b). so, continuing, we get:

    = a^2 + ab + ba + b^2 = a^2 + ab + ab + b^2 = a^2 + (ab + ab) + b^2 = a^2 + 2ab + b^2.

    this is basic, and just uses the distributive law:

    a(b+c) = ab + ac; (a+b)c = ac + bc repeatedly.
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