precalculus

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Suppose f is an even function and g is an odd function such that the composition fog is defined.d show that fog is an even function

  • precalculus -

    since f(x) is even, f(-z) = f(z)

    g(-x) = -g(x) since g is odd

    f(g(-x)) = f(-g(x)) = f(g(x)) so fog is even

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