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Math Help - Composite Function

  1. #1
    Junior Member
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    Composite Function

    Given

    f(x)=2x, where x is any real no.
    g(x)=|cos x|-cos x where 0<=x<=2 pi.

    Does composite function gf exists?
    From the domain of f,doesn't the range of f lies outside the domain of g? If it exists,why is it so and what's the domain of gf???

    Thanks a lot!
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  2. #2
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    Quote Originally Posted by cyt91 View Post
    Given

    f(x)=2x, where x is any real no.
    g(x)=|cos x|-cos x where 0<=x<=2 pi.

    Does composite function gf exists?
    From the domain of f,doesn't the range of f lies outside the domain of g? If it exists,why is it so and what's the domain of gf???

    Thanks a lot!
    The function gf will have domain equal to the set of all x in the domain of f such that f(x) is in the domain of g. Since the domain of g is given as "0<= x<= 2pi", and f just doubles x, the domain of gf is "0<= x<= pi".
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