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Math Help - Composition of Functions with a third variable

  1. #1
    Newbie KeizerSoze's Avatar
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    Composition of Functions with a third variable

    Given the functions F(x) = 2x^2 - 7 and g(x) = 2x + a, find all values of a such that the y-intercept of the graph of (f o g)(x) is (0,65)

    I understand that (f o g)(x) can be rewritten as f(g(x)) but I have never encountered another variable besides x/y to figure out in this type of question. Can someone help me get started on this one? Thank you.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Composition of Functions with a third variable

    Quote Originally Posted by KeizerSoze View Post
    Can someone help me get started on this one? Thank you.
    Find y=(f\circ g)(x)=\ldots , for x=0 , y must be 0,65 . Now, you'll have a very simple second degree equation on a .
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    Re: Composition of Functions with a third variable

    Quote Originally Posted by KeizerSoze View Post
    Given the functions F(x) = 2x^2 - 7 and g(x) = 2x + a, find all values of a such that the y-intercept of the graph of (f o g)(x) is (0,65)

    I understand that (f o g)(x) can be rewritten as f(g(x)) but I have never encountered another variable besides x/y to figure out in this type of question. Can someone help me get started on this one? Thank you.
    The fact thast you are given "f(x)" and "g(x)" indicates that the only variable in those functions is x. The "a" is a parameter- representing some numerical constant.

    f(g(x))= 2(g(x))^2- 7= 2(2x+a)^2- 7

    Can you finish that? For what value of a do you have f(g(0))= 65?
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