(本小題滿分14分)
(理)已知命題

:關(guān)于

的函數(shù)

的定義域是

;命題

:當(dāng)

時(shí),

恒成立. 如果命題“

”是真命題,“

”是假命題,求實(shí)數(shù)

的取值范圍.
(文)已知命題

:

,

;命題

:當(dāng)

時(shí),

恒成立 .如果命題“

”是真命題,“

”是假命題,求實(shí)數(shù)

的取值范圍.
(理)若

是真命題,則關(guān)于

的不等式

在
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上恒成立,所以
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時(shí),滿足題設(shè);
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時(shí),要使
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在
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上恒成立,必須

,解得

.,
綜上
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.
若
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是真命題,則
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恒成立 ,所以
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
,當(dāng)且僅當(dāng)
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,即
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時(shí)取等號(hào)。

,
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若命題“

”是真命題,“

”是假命題,則命題

和

一真一假
所以

的取值范圍是

。
(文)若

是真命題,

,

,
所以

,解得

,或

,
若

是真命題,則

恒成立 ,所以


,當(dāng)且僅當(dāng)

,即

時(shí)取等號(hào)。

,

若命題“

”是真命題,“

”是假命題,則命題

和

一真一假
所以

的取值范圍是

。
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
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(I)若
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
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,函數(shù)

恒成立,若

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
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設(shè)

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
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,如果“
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”是真命題,“

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
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命題“若

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給出下列五個(gè)命題:
①函數(shù)

的圖象與直線

可能有兩個(gè)不同的交點(diǎn);
②函數(shù)

與函數(shù)

是相等函數(shù);
③對于指數(shù)函數(shù)

與冪函數(shù)

,總存在

,當(dāng)

時(shí),有

成立;
④對于函數(shù)

,若有

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在

內(nèi)有零點(diǎn).
⑤已知

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的根,
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是方程

的根,則

.
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原命題“設(shè)

”的逆命題、否命題、逆否命題中,真命題的個(gè)數(shù)是(

)
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下列四種說法中,錯(cuò)誤的個(gè)數(shù)是
①.命題“
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”的否定是“
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” ;
②.“命題
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為真”是“命題
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為真”的必要不充分條件;
③.“若
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”的逆命題為真;
④.若實(shí)數(shù)
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,則滿足:
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的概率為
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;
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