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Last edited by hbghlyj 2025-3-19 08:14对于正实数 $\alpha$ ,记 $M_a$ 为满足下述条件的函数 $f(x)$ 构成的集合:$\forall x_1, x_2 \inR$ 且 $x_2>x_1$,有 $-\alpha\left(x_2-x_1\right)<f\left(x_2\right)-f\left(x_1\right)<\alpha\left(x_2-x_1\right)$.下列结论中正确的是( )
A.若 $f(x) \in M_{\alpha 1}, ~g(x) \in M_{\alpha 2}$ ,则 $f(x) \cdot g(x) \in M_{\alpha 1 \alpha2}$
B.若 $f(x) \in M_{\alpha 1}, ~g(x) \in M_{\alpha 2}$ ,且 $g(x) \neq 0$ ,则 $\frac{f(x)}{g(x)} \in M_{\frac{\alpha 1}{\alpha 2}}$
C.若 $f(x) \in M_{\alpha 1}, ~g(x) \in M_{\alpha 2}$ ,则 $f(x)+g(x) \in M_{\alpha 1+\alpha 2}$
D.若 $f(x) \in M_{\alpha 1}, ~g(x) \in M_{\alpha 2}$ ,且 $\alpha_1>\alpha_2$ ,则 $f(x)-g(x) \in M_{\alpha1-\alpha2}$ |
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