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Math Help - Another composition of functions question

  1. #1
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    Another composition of functions question

    The question:

    Form the composition fog and give the domain,

    f(x) = \sqrt{1 - x^2}
    g(x) = cos(2x)

    My attempt:
    (fog)(x) = \sqrt{1 - (cos(2x))^2}

    I worked out the domain of f(x) is [-1, 1], and the domain of g(x) is (-inf, inf). Thus fog must have the domain [-1, 1].

    However, the answer is:
    |sin(2x)| with domain (-inf, inf)

    What am I doing wrong? Thanks!
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  2. #2
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    Quote Originally Posted by Glitch View Post
    The question:

    Form the composition fog and give the domain,
    f(x) = \sqrt{1 - x^2}
    g(x) = cos(2x)

    My attempt:
    (fog)(x) = \sqrt{1 - (cos(2x))^2}
    I worked out the domain of f(x) is [-1, 1], and the domain of g(x) is (-inf, inf). Thus fog must have the domain [-1, 1].
    However, the answer is:
    |sin(2x)| with domain (-inf, inf)
    Note that 1-\cos^2(x)=\sin^2(x), \sqrt{(x^2)}=|x| and -1\le\sin(x)\le1.
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  3. #3
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    Ahh! I didn't recognise that trig identity! Thanks!
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