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Math Help - Find Simplified Expression for g(x)

  1. #1
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    Find Simplified Expression for g(x)

    If f(x)=2x^2-3x+1, find the simplified expression for g(x) in
    g(x)= f(2x).
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    Replace every x in f(x) with 2x.

    Then simplify.
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    Let x = 2x for f(x)

    f(2x) = 2(2x)^2-3(2x)+1

    f(2x) = 2(4x^2) - 6x + 1

    f(2x) = 8x^2 - 6x + 1

    Correct?
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    Quote Originally Posted by fdrhs1984 View Post
    Let x = 2x for f(x)

    f(2x) = 2(2x)^2-3(2x)+1

    f(2x) = 2(4x^2) - 6x + 1

    f(2x) = 8x^2 - 6x + 1

    Correct?
    Yes, good job.
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    Great! Thanks a lot.
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    Quote Originally Posted by fdrhs1984 View Post
    Let x = 2x for f(x)

    f(2x) = 2(2x)^2-3(2x)+1

    f(2x) = 2(4x^2) - 6x + 1

    f(2x) = 8x^2 - 6x + 1

    Correct?
    Yes it is.

    You could also simplify further by factorising.

    f(2x) = 8x^2 - 6x + 1

     = 8x^2 - 4x - 2x + 1

     = 4x(2x - 1) - 1(2x - 1)

     = (2x - 1)(4x - 1).
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    Is this the Grouping Method for factoring?
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    Quote Originally Posted by fdrhs1984 View Post
    Is this the Grouping Method for factoring?
    It most certainly is.

    Multiply your a and c values. In this case you get 8.

    So you need to think of two numbers that multiply to give 8 and add to give -6 (the b value). In this case they are -4 and -2, which is what you break the middle term into.
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