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show that the composition of two increasing functions is increasing

  • precalculus -

    (fog)(x) = f(g(x))
    f(x+h) > f(x) if h>0
    g(x+h) > g(x) if h>0, so g(x+h) = g(x) + k for some value of k

    consider f(g(x+h)). g(x+h) > g(x), so
    f(g(x+h)) > f(g(x))

    so, increasing

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