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Math Help - composition of functions

  1. #1
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    Question composition of functions

    Hey I have no idea how to do this question...can you point me in the right way please

    Consider the following functions:
    f(x) = x + 1, g(x) = x − 1, h(x) = 2x, m(x) = 4x, n(x) = x^2, p(x) = √x, and q(x) = 2x + 1.
    Use composition of functions and one or more of f , g, h, m, n, p and q to define two new functions: y(x) = x^2 − 2x + 1 and z(x) = 4x^2

    Thanks for any help
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by smplease View Post
    Hey I have no idea how to do this question...can you point me in the right way please

    Consider the following functions:
    f(x) = x + 1, g(x) = x − 1, h(x) = 2x, m(x) = 4x, n(x) = x^2, p(x) = √x, and q(x) = 2x + 1.
    Use composition of functions and one or more of f , g, h, m, n, p and q to define two new functions: y(x) = x^2 − 2x + 1 and z(x) = 4x^2

    Thanks for any help
    For example f(g(x))=(x-1)^2=x^2-2x+1
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by smplease View Post
    Hey I have no idea how to do this question...can you point me in the right way please

    Consider the following functions:
    f(x) = x + 1, g(x) = x − 1, h(x) = 2x, m(x) = 4x, n(x) = x^2, p(x) = √x, and q(x) = 2x + 1.
    Use composition of functions and one or more of f , g, h, m, n, p and q to define two new functions: y(x) = x^2 − 2x + 1 and z(x) = 4x^2

    Thanks for any help
    Quote Originally Posted by Mathstud28 View Post
    For example f(g(x))=(x-1)^2=x^2-2x+1
    @Mathstud 28: Where did you get that?
    f(g(x)) = f(x - 1) = (x - 1) + 1 = x

    Now
    n(g(x)) = n(x - 1) = (x - 1)^2 = x^2 - 2x + 1

    For the second problem, I would like to draw your attention to m(x) and n(x). Can you use these to form 4x^2?

    -Dan
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