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Math Help - is this a monotonic transformation of f(x)?

  1. #1
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    is this a monotonic transformation of f(x)?

    Say I have a function f(x)=\frac{1}{x}

    Would the following count as positive monotonic transformations of f(x)?

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

    What defines a positive monotonic transformation of f(x)?


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  2. #2
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    You mean monotonic increasing function.

    Then please check the condition

    <br />
g'(x)>0.<br />
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