若定義在R上的函數(shù)
f(
x)滿足:對任意
x1,
x2
R有
f(
x1+
x2)=
f(
x1)+
f(
x2)+1,,則下列說法一定正確的是( )
A.f(x)為奇函數(shù) | B.f(x)為偶函數(shù) |
C. f(x)+1為奇函數(shù) | D.f(x)+1為偶函數(shù) |
本題主要考查的是抽象函數(shù)的奇偶性。設

。所以條件中的等式變?yōu)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823191729379978.png" style="vertical-align:middle;" />,即

。令

,解得

。再令

,則

,

。所以

為奇函數(shù),即

為奇函數(shù),選C。
練習冊系列答案
相關習題
科目:高中數(shù)學
來源:不詳
題型:解答題
(12分)已知

(

)
(1)求

的定義域。
(2)判斷

與

的關系,并就此說明函數(shù)

圖像的特點。
(3)求使

的點的

的取值范圍。
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:解答題
若定義在

上的函數(shù)


滿足條件:存在實數(shù)

且



,使得:
⑴ 任取

,有

(

是常數(shù));
⑵ 對于

內(nèi)任意

,當

,總有

。
我們將滿足上述兩條件的函數(shù)

稱為“平頂型”函數(shù),稱

為“平頂高度”,稱

為“平頂寬度”。根據(jù)上述定義,解決下列問題:
(1)函數(shù)

是否為“平頂型”函

數(shù)?若是,求出“平頂高度”和“平頂寬度”;若不是,簡要說明理由。
(2) 已知

是“平頂型”函數(shù),求出

的值。
(3)對于(2)中的函數(shù)

,若

在

上有兩個不相等的根,求實數(shù)

的取值范圍。
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:單選題
已知函數(shù)

,則

=( )
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:填空題
.設偶函數(shù)

滿足

,則不等式

>0的解集為_____.
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:填空題
已知函數(shù)

是定義在

上的偶函數(shù),當

時,

,則當

時,

的解析式為
.
查看答案和解析>>