Silent Hunter 5 : Battle Of The Atlantic Full Crack [Torrent]
Silent Hunter 5 Battle Of The Atlantic – How To Install Full Pc Game in Direct Download link! : UC Play Download now! Silence. Is that enough? Not.. the .Q:
Are the following statements equivalent
$$(i) \text{ $f$ is odd and $f(x) \ge 0$ for all $x$ }$$
$$(ii) \text{ $f$ is a monotone decreasing function on $[0, + \infty)$ }$$
I know that (ii) follows from (i). But how about (i) implies (ii) (i.e. (i) $\implies$ (ii))?
A:
If $f$ is odd then so is $-f$ and hence $f$ is non-negative and its minimum is zero. So $$f(x)\geq0,\forall x\geq0,\implies f(x)\geq0,\forall x\in\mathbb R\implies f(x)\geq0,\forall x\geq 0\lor f(x)\leq0,\forall x\leq0$$
which means $f$ is a monotone decreasing function on $[0,+\infty).$
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