若定义f(x)=3x﹣2,如f(﹣2)=3×(﹣2)﹣2=﹣8,下列说法中:①当f(x)=1时,x=1;②对于正数x,f(x)>f(﹣x)均成立;③f(x﹣1)+f(1﹣x)=0;④当a=2时,f(a﹣x)=a﹣f(x).其中正确的是( )
A.①② | B.①③ | C.①②④ | D.①③④ |
更新时间:2019-09-16 22:00:25
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【知识点】 新定义下的实数运算
相似题推荐
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【推荐1】如图所示为一金字塔运算程序,其中箭头为数字的移动方向,字母表示限制条件,序号为运算方式,已知
:
;①:
;
:
;②:
;
:
;③:
;
:
;④:
;
:
;
:
,若某层中的数字达到限制条件,就可以通过相应的运算方式进入新一层,安安将输入的数字定为2,则最后输出的结果为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27f27cbb8185c1974d715ff95f8801c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171703208385075d304ab077dac23c26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1b556ada1f57e1b36d8f4f776976c0.png)
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A.![]() | B.![]() | C.![]() | D.无法得到 |
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【推荐2】对任意两个正实数
,
,定义新运算
为:若
,则
;若
,则
.则下列说法中正确的有( )
①
;②
;③
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8ec7bed2a39576b63c8730c76e85c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1132de2e8913dba9c5cc2396ecb09fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2abbd4848e96b97fb008ab1377a22f90.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df765029a6697b301249b9a75af97cc.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd43adbff32abea8d75da8292f47465a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681c7717463e3bc38ea3d4c96ac7e4ac.png)
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A.① | B.② | C.①③ | D.②③ |
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名校
【推荐3】已知两个实数
、
,可按如下规则进行运算:若
为奇数,则计算
的结果;若
为偶数,则计算
的结果.根据上述规则,每得到一个数叫做一次操作.对于给定的两个实数
、
,操作一次后得到的数记为
;再从
、
、
中任选两个数,操作一次得到的数记为
;再从
、
、
、
中任选两个数,操作一次得到的数记为
,依次进行下去……以下结论正确的个数为( )
①若
,
,则
;
②若
、
为方程
的两根,则
;
③若
、
均为奇数,则无论进行多少次操作,得到的
均不可能为偶数;
④若
,
,要使得
成立,则
至少为4.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db84454f051d418a4904fa423ab8b304.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7612f7cc117e8bb1b9e6a1701649aff.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41527a0e6cee74e1177777a168ec81de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07406516c9cbed73d1b88a5f1c17e839.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3320a13248a3a1208ff6ee85c9d26f36.png)
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A.1 | B.2 | C.3 | D.4 |
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