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

1. ## 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)?

Thanks

2. You mean monotonic increasing function.

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