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Thread: 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 $\displaystyle f(x)=\frac{1}{x}$

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

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

    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

    $\displaystyle
    g'(x)>0.
    $
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