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    Proof real exponentiation

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    Let x,y > 0 be positive reals, and let n, m >= 1 be positive integers,
    Prove:
    If x > 1, then x ^ 1/k is a decreasing function of k. If x < 1, then x ^ 1/k is an increasing function of k. If x=1, then x ^ 1/k = 1 for all k.

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    https://brainmass.com/math/real-analysis/proof-real-exponentiation-468277

    Solution Preview

    Let x,y > 0 be positive reals, and let n, m >= 1 be positive integers,
    Prove:
    If x > 1, then x ^ 1/k is a decreasing function of k. If x < 1, then x ^ 1/k is an increasing function of k. If x=1, then x ^ 1/k = 1 for all k.

    We recall the definition of an increasing function.
    A function f is said to be an ...

    Solution Summary

    The expert examines proof real exponentiation.

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