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Thread: Analysis Proof involving compositon f o g.

  1. #1
    Junior Member
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    Analysis Proof involving compositon f o g.

    If f and g are defined for all x and are odd or even (four possibilities altogether), what can be said about the composition $\displaystyle f \circ g$? Prove it.

    I'm not sure what can be said about the composition or what the four possiblilities should be.

    Help is appreciated.
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  2. #2
    Senior Member
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    Suppose f and g are even. Then f(g(-x)) = f(g(x) so f(g) is even. If f and g are both odd, then f(g(-x)) = f(-g(x))=-f(g(x)), so f(g) is odd. You try the other two.
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