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Math Help - Domain and range of composed functions

  1. #1
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    Domain and range of composed functions

    The functions f and g have domains (0,inf) and (2,inf) respectively and are defined by

    f(x) = x^2 - 1
    g(x) = 2x - 1

    a] write down the ranges of f and g.

    range of f = (-1 , inf)
    range of g = (3, inf)

    b] give the reason why gf(1) cannot be formed.

    Because 1 is not in the domain of g.

    c] find a simplified expression for fg(x)

    = 4x^2 - 4x

    d] state the domain and range of fg.

    domain = (2, inf)
    range = (8, inf)

    Do you believe that my answers correct? These were from an exam and I am hoping that they were correct. Thanks
    PS - take inf to mean infinity!
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  2. #2
    Junior Member
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    Illinois
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    Pretty good.
    gf(1) cannot be formed, using your notation for function composition, because f(1) is not in the domain of g, not because 1 is not in g's domain.

    g(f(1)) would be better notation
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