 Strictly decreasing function

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.