= Strictly decreasing function
{title2=$x<y\implies f(x)>f(y)$}
= Strictly decreasing
{synonym}
A <real-valued function> $f:D\to\mathbb R$ is a <strictly decreasing function> if every pair $x<y$ in its <domain of a function> satisfies $f(x)>f(y)$. It is a <nonincreasing function> and is <injective>, with a <strictly decreasing> <inverse function> on its <image of a function>. Negating a <strictly increasing function> gives a <strictly decreasing function>: $f(x)=-x^3$ is an example on the <real line>, even though its <derivative> vanishes at zero. Equal outputs are forbidden, unlike for a general <nonincreasing function>.
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