提问于:
浏览数:
2143
\documentclass{book}%文档格式
\RequirePackage[a4paper]{geometry}
\geometry{
textwidth=138mm, textheight=215mm, left=15mm, right=10mm, top=10mm,
bottom=5mm, headheight=2.17cm, headsep=4mm, footskip=12mm, heightrounded,}
%设置页边距
\usepackage{amsmath}%数学公式
\usepackage{ctex}%输出汉字
\usepackage{graphicx}%插入图片
\usepackage{tikz}%画图用
\pagestyle{myheadings}
\markboth{*}{数列}%设置页眉及页码
\usepackage{multicol}%分栏
\usepackage{newtxmath}%接近于mathtype字体
\usepackage{ifthen}
\newlength{\la}
\newlength{\lb}
\newlength{\lc}
\newlength{\ld}
\newlength{\lhalf}
\newlength{\lquarter}
\newlength{\lmax}
\newcommand{\xx}[4]{\\[.5pt]%
\settowidth{\la}{A.~#1~~~}
\settowidth{\lb}{B.~#2~~~}
\settowidth{\lc}{C.~#3~~~}
\settowidth{\ld}{D.~#4~~~}
\ifthenelse{\lengthtest{\la > \lb}} {\setlength{\lmax}{\la}} {\setlength{\lmax}{\lb}}
\ifthenelse{\lengthtest{\lmax < \lc}} {\setlength{\lmax}{\lc}} {}
\ifthenelse{\lengthtest{\lmax < \ld}} {\setlength{\lmax}{\ld}} {}
\setlength{\lhalf}{0.5\linewidth}
\setlength{\lquarter}{0.25\linewidth}
\ifthenelse{\lengthtest{\lmax > \lhalf}} {\noindent{}A.~#1 \\ B.~#2 \\ C.~#3 \\ D.~#4 } {
\ifthenelse{\lengthtest{\lmax > \lquarter}} {\noindent\makebox[\lhalf][l]{A.~#1~~~}%
\makebox[\lhalf][l]{B.~#2~~~}%
\makebox[\lhalf][l]{C.~#3~~~}%
\makebox[\lhalf][l]{D.~#4~~~}}%
{\noindent\makebox[\lquarter][l]{A.~#1~~~}%
\makebox[\lquarter][l]{B.~#2~~~}%
\makebox[\lquarter][l]{C.~#3~~~}%
\makebox[\lquarter][l]{D.~#4~~~}}}}%选项自动识别长度
\newcommand{\kh}{\nolinebreak\dotfill\mbox{\raisebox{-1.8pt}
{$\cdots$}(\hspace{0.3cm})}}
\begin{document}
\begin{multicols}{2}%分栏加中间线
\columnseprule=1pt%加中间线
\begin{enumerate}
\item 设$ f(x) = \ln (\sqrt {{{(x + 1)}^2}} + x + 1) - 2 $,若$ f(a) = 1 $,$ f(b) = - 5 $,则$ a+b= $\kh
\xx{$ 2 $}{$ 0 $}{$ 1 $}{$ -2 $}%1
\item 设函数$ f(x) = \frac{{{x^5} + {{(x + 1)}^2}}}{{{x^2} + 1}} $在区间$ \left[ { - 12,12} \right] $上的最大值为$ M $,最小值为$ N $,则$ {(M + n - 1)^{2019}} $的值为\kh
\xx{$ 1 $}{$ -1 $}{$ 2^{2019} $}{$ 0 $}%2
\item 已知函数$ f(x) = \frac{{{2^x}}}{{{2^x} - 1}} $,若$ f(-m)=2 $,则$ f(m)= $\kh
\xx{$ -2 $}{$ -1 $}{$ 0 $}{$ \frac{1}{2} $}%3
\item 已知函数$ y=f(x)+x $是偶函数,且$ f(2)=1 $,则$ f(-2)= $\kh
\xx{$ 2 $}{$ 3 $}{$ 4 $}{$ 5 $}%4
\item 已知$ f(x)=g(x)-4 $,函数$ g(x) $是定义在$ R $上的奇函数,若$ f(2017)=2017 $,则$ f(-2017)= $\kh
\xx{$ -2017 $}{$ -2021 $}{$ -2025 $}{$ 2025 $}%5
\item 已知函数$ f(x) $是定义在$ R $上的偶函数,且在$ \left[ {0, + \infty } \right) $上是减函数,则满足$ f(a-1)>f(1) $的实数$ a $的取值范围是\kh
\xx{$ ({\rm{2, + }}\infty ) $}{$ ( - \infty ,2) $}{$ ({\rm{0,2}}) $}{$({\rm{1,2}}) $}%6
\item 已知$ f(x) $为偶函数,其在$ ( - \infty ,0] $上为增函数,$ f(2)=0 $,满足不等式$ f(1-x)<0 xss=removed>f(2) $的解集为\kh
\xx{$ (-1,1) $}{$ (-4,2) $}{$ ( - \infty , - 1) \cup ({\rm{1, + }}\infty ) $}{$ ( - \infty , - 4) \cup ({\rm{2, + }}\infty ) $}%8
\item 已知$ f(x) = \frac{{2x + 1}}{{x - 1}} + {(x - 1)^3} $,若$ f(2018)=a $,则$ f(-2016)= $\kh
\xx{$ -a $}{$ 2-a $}{$ 4-a $}{$ 1-a$}%9
\item 已知函数$ f(x) = {e^{|x|}} + \cos x $,若$ f(2x-1)\le f(x) $,则实数$ x $的取值范围是\kh
\xx{$ ( - \infty , \frac{1}{3}] \cup [{\rm{1, + }}\infty ) $}{$ [\frac{1}{3},1] $}{$ ( - \infty , \frac{1}{2}] $}{$ [{\rm{\frac{1}{2}, + }}\infty ) $}
\item 已知函数$ f(x) = x\ln (x + \sqrt {{x^2} + 1} ) $,若$ f(2a-1)1 $}{$ a<0>1 $}{$ 0 0 $的解集为\kh
\xx{$ ( - \infty , - 3] \cup (0,3) $}{$ ( - \infty , - 3) \cup (3{\rm{, + }}\infty ) $}{$ ( - 3,0) \cup (0,3) $}{$ ( - 3,0) \cup (3{\rm{, + }}\infty ) $}
\item 已知函数$ f(x)=\sqrt{x-2} $,若$ f(2{a^2} - 5a + 4) < f xss=removed xss=removed xss=removed xss=removed>4 $的解集为\kh
\xx{$ (-\frac{1}{4},+\infty) $}{$ (-\infty,-\frac{1}{4}) $}{$ (-\infty,0) $}{$ (0,+\infty) $}
\item 设$ f(x) = {2^x} - {2^{ - x}} + \ln \frac{{1 + x}}{{1 - x}} + 1 $,若$ f(a)+f(1+a)>2 $,则$ a $的取值范围\kh
\xx{$ (-\frac{1}{2},+\infty) $}{$ (-\frac{1}{2},1) $}{$ (-\frac{1}{2},0) $}{$ (0,\frac{1}{2}) $}!
\item 已知定义在$ R $上的奇函数$ f(x) $,任意$ x_{1} ,x_{2}\in [0{\rm{, + }}\infty ) $,且$x_{1} \ne x_{2}$都有
$ \frac{{f({x_1}) - f({x_2})}}{{{x_1} - {x_2}}} < 0> 0} $,若$ f(2)=0 $,则$ (x-2)f(x)>0 $的解集为\kh
\xx{$\left( {-\infty,-2}\right) \cup\left( {0,2}\right) \cup\left( {2,+\infty}\right) $}{$\left( {-2,0}\right) \cup\left( {0, + \infty}\right)$ }{$\left( {-\infty,-2}\right) \cup\left( {0,2}\right) $}{$\left( {-2,0}\right) \cup(0,2)$}#
\item 已知函数$ f(x) $满足$ f(x)=f(-x+2) $,且$ f(x) $在$ ( - \infty , 1] $上单调递增,则\kh
\xx{$ f(1) > f( - 1) > f(4) $}{$ f(-1) > f( 1) > f(4) $}{$ f(4) > f( 1) > f(-1) $}{$ f(1) > f( 4) > f(-1) $}$
\item 函数$ f(x) = \sqrt {{x^2} - x + 2} $的单调递增区间为\kh
\xx{$ [2, + \infty ) $}{$ ( - \infty ,\frac{1}{2}] $}{$ [\frac{1}{2}, + \infty ) $}{$ ( - \infty ,-1] $}%
\item 函数$ f(x) = {\log _{0.6}}({x^2} + 6x - 7) $的单调递减区间是\kh
\xx{$ ( - \infty ,-7) $}{$ ( - \infty ,-3) $}{$ (-3, + \infty ) $}{$ (1, + \infty ) $}&
\item 若定义在$ R $上的函数$ f(x) $满足:$ x \in ( - 3, - 1) $时,$ f(x+1)=e^{x} $,对于任意$ x\in R $,都有
$ f(x + 2) = \frac{1}{{f(x)}} $成立,$ f(2019)= $\kh
\xx{$ e^{2} $}{$ e^{-2} $}{$ e $}{$ 1 $}'
\item 若定义在$ R $上的函数$ f(x) $满足$ f(-x)=f(x) $,$ f(x+1)=f(1-x) $,且当$ x\in [0,1] $时,$ f(x) = {\log _2}(x + 1) $,则$ f((2019)= $\kh
\xx{$ 0 $}{$ 1 $}{$ -1 $}{$ 2 $}(
\item 若定义在$ R $上的函数$ f(x) $满足$ f(-x)=-f(x) $,$ f(x)=f(x+2) $,且当$ x\in (-1,0) $时,$ f(x) = {2^x} + \frac{1}{3} $,则$ f({\log _2}6) = $\kh
\xx{$ 1 $}{$ -1 $}{$ \frac{4}{5} $}{$ -\frac{4}{5} $})
\item 若定义在$ R $上的函数$ f(x) $满足$ f(x)=-f(x+1) $,且当$ 1\le x<2 $时,$ f(x) = {9^x} - 9 $,则$ f( - \frac{1}{2}) = $\kh
\xx{$ 0 $}{$ -6 $}{$ 18 $}{$ -18 $}0
\item 已知函数$ f(x) $对于任意实数$ x $满足条件$ f(x + 2) = - \frac{1}{{f(x)}} $,若$ f(0)=\frac{1}{2} $,则$ f(2018)= $\kh
\xx{$ -\frac{1}{2} $}{$ \frac{1}{2} $}{$ -2 $}{$ 2 $}1
\item 已知函数$ y=f(x) $满足$ f(x + 1) = \frac{1}{{f(x - 1)}} $和$ f(2-x)=f(x+1) $,且当$ x \in [\frac{1}{2},\frac{3}{2}] $时,$ f(x)=2x+2 $,则$ f(2018)= $\kh
\xx{$ 0 $}{$ 2 $}{$ 4 $}{$ 5 $}2
\item 若定义在$ R $上的偶函数$ f(x) $,对任意的实数$ x $都有$ f(x+4)=-f(x)+2 $,且$ f(-3)=3 $,则$ f(2015)= $\kh
\xx{$ -1 $}{$ 3 $}{$ 2015 $}{$ -4028 $}3
\item 若定义在$ R $上的函数$ f(x) $满足对任意$ x\in R $,有$ f(x + 2) = \frac{1}{{f(x)}} $,且$ f(x) $的图像关于直线$ x=1 $对称,当$ x\in [-1,1] $时,$ f(x)=x+1 $,则$ f(6)= $\kh
\xx{$ 1 $}{$ 2 $}{$ 3 $}{$ 4 $}4
\item 设定义在$ R $上的函数$ f(x) $满足$ f(x) \cdot f(x + 2) = 13 $,若$ f(1)=2 $,则$ f(2015)= $\kh
\xx{$ \frac{13}{3} $}{$ \frac{13}{2} $}{$ 13 $}{$ \frac{39}{2} $}5
\item 定义在$ R $上的偶函数$ f(x) $满足:对任意的实数$ x $都有$ f(-x)=f(x+2) $,$ f(-1)=2 $,$ f(2)=-1 $,则$ f(1) + f(2) + f(3) + \cdot \cdot \cdot + f(2017) $的值为\kh
\xx{$ 2017 $}{$ 1010 $}{$ 1008 $}{$ 2 $}6
\item 已知函数$ f(x) $是定义在$ R $上的奇函数,$ f(\frac{3}{2}+x)=f(\frac{3}{2}-x) $,且$ x\in (-\frac{3}{2},0) $时,$ f(x) = {\log _2}( - 3x + 1) $,则$ f(2020)= $\kh
\xx{$ 4 $}{$ log_{2}7 $}{$ 2 $}{$ -2 $}7
\item 定义在$ R $上的奇函数$ f(x) $满足$ f(1+x)=f(1-x) $,且当$ x\in [0,1] $时,$ f(x)=x(3-2x) $,则$ f(\frac{31}{2})= $\kh
\xx{$ -1 $}{$ -\frac{1}{2}$}{$ \frac{1}{2} $}{$ 1 $}8
\item 已知函数$ f(x) = {\log _{\frac{1}{3}}}(3{x^2} - ax + 8) $在$ \left[ { - 1, + \infty } \right) $上是减函数,则实数$ a $的取值范围\kh
\xx{$ ( - \infty , - 6] $}{$ [ - 11, - 6] $}{$ ( - 11, - 6] $}{$ ( - 11, + \infty )$}9
\item 已知函数$ f(x) = x + 2\sin (x - \frac{1}{2}) $,则$ f(\frac{1}{{2019}}) + f(\frac{2}{{2019}}) + \cdot \cdot \cdot + f(\frac{{2018}}{{2019}}) $的值等于\kh
\xx{$ 2019 $}{$ 2018 $}{$ \frac{2019}{2} $}{$ 1009 $}@
\end{enumerate}
\end{multicols}%分栏 加中间线
\end{document}![](https://pics.latexstudio.net/data/images/202001/2ef0ac15a59a2d8.png)
2 回答
0
问题原因:
换行是两个\\\。
修改后的结果:
![](https://pics.latexstudio.net/data/images/202001/d84279af745d143.png)
作者追问:2020-01-13 10:46
```tex
\documentclass{book}%文档格式
\RequirePackage[a4paper]{geometry}
\geometry{
textwidth=138mm, textheight=215mm, left=15mm, right=10mm, top=10mm,
bottom=5mm, headheight=2.17cm, headsep=4mm, footskip=12mm, heightrounded,}
%设置页边距
\usepackage{amsmath}%数学公式
\usepackage{ctex}%输出汉字
\usepackage{graphicx}%插入图片
\usepackage{tikz}%画图用
\pagestyle{myheadings}
\markboth{由文龙}{数列}%设置页眉及页码
\usepackage{multicol}%分栏
\usepackage{newtxmath}%接近于mathtype字体
\usepackage{ifthen}
\newlength{\la}
\newlength{\lb}
\newlength{\lc}
\newlength{\ld}
\newlength{\lhalf}
\newlength{\lquarter}
\newlength{\lmax}
\newcommand{\xx}[4]{\\[.5pt]%
\settowidth{\la}{A.~#1~~~}
\settowidth{\lb}{B.~#2~~~}
\settowidth{\lc}{C.~#3~~~}
\settowidth{\ld}{D.~#4~~~}
\ifthenelse{\lengthtest{\la > \lb}} {\setlength{\lmax}{\la}} {\setlength{\lmax}{\lb}}
\ifthenelse{\lengthtest{\lmax < \lc}} {\setlength{\lmax}{\lc}} {}
\ifthenelse{\lengthtest{\lmax < \ld}} {\setlength{\lmax}{\ld}} {}
\setlength{\lhalf}{0.5\linewidth}
\setlength{\lquarter}{0.25\linewidth}
\ifthenelse{\lengthtest{\lmax > \lhalf}} {\noindent{}A.~#1 \\ B.~#2 \\ C.~#3 \\ D.~#4 } {
\ifthenelse{\lengthtest{\lmax > \lquarter}} {\noindent\makebox[\lhalf][l]{A.~#1~~~}%
\makebox[\lhalf][l]{B.~#2~~~}%
\makebox[\lhalf][l]{C.~#3~~~}%
\makebox[\lhalf][l]{D.~#4~~~}}%
{\noindent\makebox[\lquarter][l]{A.~#1~~~}%
\makebox[\lquarter][l]{B.~#2~~~}%
\makebox[\lquarter][l]{C.~#3~~~}%
\makebox[\lquarter][l]{D.~#4~~~}}}}%选项自动识别长度
\newcommand{\kh}{\nolinebreak\dotfill\mbox{\raisebox{-1.8pt}
{$\cdots$}(\hspace{0.3cm})}}
\begin{document}
\begin{multicols}{2}%分栏加中间线
\columnseprule=1pt%加中间线
\begin{enumerate}
\item[一、] 选择题
\item 设$ f(x) = \ln (\sqrt {{{(x + 1)}^2}} + x + 1) - 2 $,若$ f(a) = 1 $,$ f(b) = - 5 $,则$ a+b= $\kh
\xx{$ 2 $}{$ 0 $}{$ 1 $}{$ -2 $}%1
\item 设函数$ f(x) = \frac{{{x^5} + {{(x + 1)}^2}}}{{{x^2} + 1}} $在区间$ \left[ { - 12,12} \right] $上的最大值为$ M $,最小值为$ N $,则$ {(M + n - 1)^{2019}} $的值为\kh
\xx{$ 1 $}{$ -1 $}{$ 2^{2019} $}{$ 0 $}%2
\item 已知函数$ f(x) = \frac{{{2^x}}}{{{2^x} - 1}} $,若$ f(-m)=2 $,则$ f(m)= $\kh
\xx{$ -2 $}{$ -1 $}{$ 0 $}{$ \frac{1}{2} $}%3
\item 已知函数$ y=f(x)+x $是偶函数,且$ f(2)=1 $,则$ f(-2)= $\kh
\xx{$ 2 $}{$ 3 $}{$ 4 $}{$ 5 $}%4
\item 已知$ f(x)=g(x)-4 $,函数$ g(x) $是定义在$ R $上的奇函数,若$ f(2017)=2017 $,则$ f(-2017)= $\kh
\xx{$ -2017 $}{$ -2021 $}{$ -2025 $}{$ 2025 $}%5
\item 已知函数$ f(x) $是定义在$ R $上的偶函数,且在$ \left[ {0, + \infty } \right) $上是减函数,则满足$ f(a-1)>f(1) $的实数$ a $的取值范围是\kh
\xx{$ ({\rm{2, + }}\infty ) $}{$ ( - \infty ,2) $}{$ ({\rm{0,2}}) $}{$({\rm{1,2}}) $}%6
\item 已知$ f(x) $为偶函数,其在$ ( - \infty ,0] $上为增函数,$ f(2)=0 $,满足不等式$ f(1-x)<0 xss=removed>f(2) $的解集为\kh
\xx{$ (-1,1) $}{$ (-4,2) $}{$ ( - \infty , - 1) \cup ({\rm{1, + }}\infty ) $}{$ ( - \infty , - 4) \cup ({\rm{2, + }}\infty ) $}%8
\item 已知$ f(x) = \frac{{2x + 1}}{{x - 1}} + {(x - 1)^3} $,若$ f(2018)=a $,则$ f(-2016)= $\kh
\xx{$ -a $}{$ 2-a $}{$ 4-a $}{$ 1-a$}%9
\item 已知函数$ f(x) = {e^{|x|}} + \cos x $,若$ f(2x-1)\le f(x) $,则实数$ x $的取值范围是\kh
\xx{$ ( - \infty , \frac{1}{3}] \cup [{\rm{1, + }}\infty ) $}{$ [\frac{1}{3},1] $}{$ ( - \infty , \frac{1}{2}] $}{$ [{\rm{\frac{1}{2}, + }}\infty ) $}
\item 已知函数$ f(x) = x\ln (x + \sqrt {{x^2} + 1} ) $,若$ f(2a-1)1 $}{$ a<0>1 $}{$ 0 0 $的解集为\kh
\xx{$ ( - \infty , - 3] \cup (0,3) $}{$ ( - \infty , - 3) \cup (3{\rm{, + }}\infty ) $}{$ ( - 3,0) \cup (0,3) $}{$ ( - 3,0) \cup (3{\rm{, + }}\infty ) $}
\item 已知函数$ f(x)=\sqrt{x-2} $,若$ f(2{a^2} - 5a + 4) < f xss=removed xss=removed xss=removed xss=removed>4 $的解集为\kh
\xx{$ (-\frac{1}{4},+\infty) $}{$ (-\infty,-\frac{1}{4}) $}{$ (-\infty,0) $}{$ (0,+\infty) $}
\item 设$ f(x) = {2^x} - {2^{ - x}} + \ln \frac{{1 + x}}{{1 - x}} + 1 $,若$ f(a)+f(1+a)>2 $,则$ a $的取值范围\kh
\xx{$ (-\frac{1}{2},+\infty) $}{$ (-\frac{1}{2},1) $}{$ (-\frac{1}{2},0) $}{$ (0,\frac{1}{2}) $}!
\item 已知定义在$ R $上的奇函数$ f(x) $,任意$ x_{1} ,x_{2}\in [0{\rm{, + }}\infty ) $,且$x_{1} \ne x_{2}$都有
$ \frac{{f({x_1}) - f({x_2})}}{{{x_1} - {x_2}}} < 0> 0} $,若$ f(2)=0 $,则$ (x-2)f(x)>0 $的解集为\kh
\xx{$\left( {-\infty,-2}\right) \cup\left( {0,2}\right) \cup\left( {2,+\infty}\right) $}{$\left( {-2,0}\right) \cup\left( {0, + \infty}\right)$ }{$\left( {-\infty,-2}\right) \cup\left( {0,2}\right) $}{$\left( {-2,0}\right) \cup(0,2)$}#
\item 已知函数$ f(x) $满足$ f(x)=f(-x+2) $,且$ f(x) $在$ ( - \infty , 1] $上单调递增,则\kh
\xx{$ f(1) > f( - 1) > f(4) $}{$ f(-1) > f( 1) > f(4) $}{$ f(4) > f( 1) > f(-1) $}{$ f(1) > f( 4) > f(-1) $}$
\item 函数$ f(x) = \sqrt {{x^2} - x + 2} $的单调递增区间为\kh
\xx{$ [2, + \infty ) $}{$ ( - \infty ,\frac{1}{2}] $}{$ [\frac{1}{2}, + \infty ) $}{$ ( - \infty ,-1] $}%
\item 函数$ f(x) = {\log _{0.6}}({x^2} + 6x - 7) $的单调递减区间是\kh
\xx{$ ( - \infty ,-7) $}{$ ( - \infty ,-3) $}{$ (-3, + \infty ) $}{$ (1, + \infty ) $}&
\item 若定义在$ R $上的函数$ f(x) $满足:$ x \in ( - 3, - 1) $时,$ f(x+1)=e^{x} $,对于任意$ x\in R $,都有
$ f(x + 2) = \frac{1}{{f(x)}} $成立,$ f(2019)= $\kh
\xx{$ e^{2} $}{$ e^{-2} $}{$ e $}{$ 1 $}'
\item 若定义在$ R $上的函数$ f(x) $满足$ f(-x)=f(x) $,$ f(x+1)=f(1-x) $,且当$ x\in [0,1] $时,$ f(x) = {\log _2}(x + 1) $,则$ f((2019)= $\kh
\xx{$ 0 $}{$ 1 $}{$ -1 $}{$ 2 $}(
\item 若定义在$ R $上的函数$ f(x) $满足$ f(-x)=-f(x) $,$ f(x)=f(x+2) $,且当$ x\in (-1,0) $时,$ f(x) = {2^x} + \frac{1}{3} $,则$ f({\log _2}6) = $\kh
\xx{$ 1 $}{$ -1 $}{$ \frac{4}{5} $}{$ -\frac{4}{5} $})
\item 若定义在$ R $上的函数$ f(x) $满足$ f(x)=-f(x+1) $,且当$ 1\le x<2 $时,$ f(x) = {9^x} - 9 $,则$ f( - \frac{1}{2}) = $\kh
\xx{$ 0 $}{$ -6 $}{$ 18 $}{$ -18 $}0
\item 已知函数$ f(x) $对于任意实数$ x $满足条件$ f(x + 2) = - \frac{1}{{f(x)}} $,若$ f(0)=\frac{1}{2} $,则$ f(2018)= $\kh
\xx{$ -\frac{1}{2} $}{$ \frac{1}{2} $}{$ -2 $}{$ 2 $}1
\item 已知函数$ y=f(x) $满足$ f(x + 1) = \frac{1}{{f(x - 1)}} $和$ f(2-x)=f(x+1) $,且当$ x \in [\frac{1}{2},\frac{3}{2}] $时,$ f(x)=2x+2 $,则$ f(2018)= $\kh
\xx{$ 0 $}{$ 2 $}{$ 4 $}{$ 5 $}2
\item 若定义在$ R $上的偶函数$ f(x) $,对任意的实数$ x $都有$ f(x+4)=-f(x)+2 $,且$ f(-3)=3 $,则$ f(2015)= $\kh
\xx{$ -1 $}{$ 3 $}{$ 2015 $}{$ -4028 $}3
\item 若定义在$ R $上的函数$ f(x) $满足对任意$ x\in R $,有$ f(x + 2) = \frac{1}{{f(x)}} $,且$ f(x) $的图像关于直线$ x=1 $对称,当$ x\in [-1,1] $时,$ f(x)=x+1 $,则$ f(6)= $\kh
\xx{$ 1 $}{$ 2 $}{$ 3 $}{$ 4 $}4
\item 设定义在$ R $上的函数$ f(x) $满足$ f(x) \cdot f(x + 2) = 13 $,若$ f(1)=2 $,则$ f(2015)= $\kh
\xx{$ \frac{13}{3} $}{$ \frac{13}{2} $}{$ 13 $}{$ \frac{39}{2} $}5
\item 定义在$ R $上的偶函数$ f(x) $满足:对任意的实数$ x $都有$ f(-x)=f(x+2) $,$ f(-1)=2 $,$ f(2)=-1 $,则$ f(1) + f(2) + f(3) + \cdot \cdot \cdot + f(2017) $的值为\kh
\xx{$ 2017 $}{$ 1010 $}{$ 1008 $}{$ 2 $}6
\item 已知函数$ f(x) $是定义在$ R $上的奇函数,$ f(\frac{3}{2}+x)=f(\frac{3}{2}-x) $,且$ x\in (-\frac{3}{2},0) $时,$ f(x) = {\log _2}( - 3x + 1) $,则$ f(2020)= $\kh
\xx{$ 4 $}{$ log_{2}7 $}{$ 2 $}{$ -2 $}7
\item 定义在$ R $上的奇函数$ f(x) $满足$ f(1+x)=f(1-x) $,且当$ x\in [0,1] $时,$ f(x)=x(3-2x) $,则$ f(\frac{31}{2})= $\kh
\xx{$ -1 $}{$ -\frac{1}{2}$}{$ \frac{1}{2} $}{$ 1 $}8
\item 已知函数$ f(x) = {\log _{\frac{1}{3}}}(3{x^2} - ax + 8) $在$ \left[ { - 1, + \infty } \right) $上是减函数,则实数$ a $的取值范围\kh
\xx{$ ( - \infty , - 6] $}{$ [ - 11, - 6] $}{$ ( - 11, - 6] $}{$ ( - 11, + \infty )$}9
\item 已知函数$ f(x) = x + 2\sin (x - \frac{1}{2}) $,则$ f(\frac{1}{{2019}}) + f(\frac{2}{{2019}}) + \cdot \cdot \cdot + f(\frac{{2018}}{{2019}}) $的值等于\kh
\xx{$ 2019 $}{$ 2018 $}{$ \frac{2019}{2} $}{$ 1009 $}@
\item 12
\xx{我我我我我我我我我我我}{我我我我我我我我我我我}{我我我我我我我我我我我}{我我我我我我我我我我我}
\end{enumerate}
\end{multicols}%分栏 加中间线
\end{document}
```
回答: 2020-01-13 11:03
```tex
\documentclass{book}%文档格式
\RequirePackage[a4paper]{geometry}
\geometry{
textwidth=138mm, textheight=215mm, left=15mm, right=10mm, top=10mm,
bottom=5mm, headheight=2.17cm, headsep=4mm, footskip=12mm, heightrounded,}
%设置页边距
\usepackage{amsmath}%数学公式
\usepackage{ctex}%输出汉字
\usepackage{graphicx}%插入图片
\usepackage{tikz}%画图用
\pagestyle{myheadings}
\markboth{*}{数列}%设置页眉及页码
\usepackage{multicol}%分栏
\usepackage{printlen}
\usepackage{newtxmath}%接近于mathtype字体
\usepackage{ifthen}
\newlength{\la}
\newlength{\lb}
\newlength{\lc}
\newlength{\ld}
\newlength{\lhalf}
\newlength{\lquarter}
\newlength{\lmax}
\newcommand{\xx}[4]{%
\settowidth{\la}{A.~#1~}
\settowidth{\lb}{B.~#2~}
\settowidth{\lc}{C.~#3~}
\settowidth{\ld}{D.~#4~}
\ifthenelse{\lengthtest{\la > \lb}} {\setlength{\lmax}{\la}} {\setlength{\lmax}{\lb}}
\ifthenelse{\lengthtest{\lmax < \lc}} {\setlength{\lmax}{\lc}} {}
\ifthenelse{\lengthtest{\lmax < \ld}} {\setlength{\lmax}{\ld}} {}
\setlength{\lhalf}{0.5\linewidth}
\setlength{\lquarter}{0.25\linewidth}
\ifthenelse{\lengthtest{\lmax > \lhalf}} {\noindent{}A.~#1 \\ B.~#2 \\C.~#3 \\ D.~#4 } {
\ifthenelse{\lengthtest{\lmax > \lquarter}} {\noindent\makebox[\lhalf][l]{A.~#1~}%
\makebox[\lhalf][l]{B.~#2~}%
\\%这里少了换行
\makebox[\lhalf][l]{C.~#3~}%
\makebox[\lhalf][l]{D.~#4~}}
{\noindent\makebox[\lquarter][l]{A.~#1~}%
\makebox[\lquarter][l]{B.~#2~}%
\makebox[\lquarter][l]{C.~#3~}%
\makebox[\lquarter][l]{D.~#4~}}%
}
}%选项自动识别长度
\newcommand{\kh}{\nolinebreak\dotfill\mbox{\raisebox{-1.8pt}
{$\cdots$}(\hspace{0.3cm})}}
\begin{document}
\begin{multicols}{2}%分栏加中间线
\columnseprule=1pt%加中间线
\xx{我我我我我我我我我我我}{我我我我我我我我我我我}{我我我我我我我我我我我}{我我我我我我我我我我我}
\xx{我我我我我}{我我}{我我我}{我我我我}
\xx{我我}{我}{我}{我}
\end{multicols}%分栏 加中间线
\end{document}
```
-
回复 undefined :第二题里面的N大小写混了,应该都是大写的吧。 – vic156 2020-01-13 11:12 回复
-
非常感谢! – ywl_wm 2020-01-13 11:06 回复
-
回复 undefined :非常非常感谢 解决了 – ywl_wm 2020-01-13 11:06 回复
-
回复 undefined :38行 – vic156 2020-01-13 11:06 回复
-
回复 undefined :加在什么位置,能麻烦你发下代码吗 谢谢了 – ywl_wm 2020-01-13 10:59 回复
-
回复 undefined :你是说不会出现4个选项排两行的情况吗,那个是因为前面这个分支也少写了换行符号\\ – vic156 2020-01-13 10:57 回复
-
如果我把选项A的内容换成好多好多字的时候不用换行符也是你给的图片的结果,但是稍微短一点的时候就是我之前发的图片的样式了 – ywl_wm 2020-01-13 10:43 回复
0
用代码块再编辑一遍吧 [https://wenda.latexstudio.net/q-1541.html](https://wenda.latexstudio.net/q-1541.html)
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