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复合函数的定义域和值域

tag-icon • tag-icon tikz-pgf diagrams
复合函数的定义域和值域

我想在 TeX 中绘制以下内容，但是我对 tikz 还很陌生，因此我不知道。

我想给出复合函数的定义域和值域的几何解释。我该怎么做？

提前谢谢您。如能得到任何帮助，我将不胜感激。在此处输入图片描述

答案1

在此处输入图片描述

使用 Mathcha 完成的绘图：https://www.mathcha.io/editor

\documentclass[a4paper,12pt]{article}
\usepackage{tikz}


\begin{document}
\tikzset{every picture/.style={line width=0.75pt}} %set default line width to 0.75pt        

\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1]
%uncomment if require: \path (0,486); %set diagram left start at 0, and has height of 486

%Shape: Polygon Curved [id:ds15874517856748693] 
\draw  [fill={rgb, 255:red, 1; green, 204; blue, 153 }  ,fill opacity=1 ][line width=1.5]  (62,169.6) .. controls (89,158.6) and (112,155.6) .. (161,184.6) .. controls (210,213.6) and (149,221.6) .. (169,251.6) .. controls (189,281.6) and (68,307.6) .. (49,275.6) .. controls (30,243.6) and (64.88,248.85) .. (68,227.6) .. controls (71.13,206.35) and (35,180.6) .. (62,169.6) -- cycle ;
%Shape: Polygon Curved [id:ds7831539165095052] 
\draw  [fill={rgb, 255:red, 204; green, 0; blue, 1 }  ,fill opacity=1 ][line width=1.5]  (258,157.6) .. controls (285,146.6) and (321,160.6) .. (357,172.6) .. controls (393,184.6) and (369,195.6) .. (365,239.6) .. controls (361,283.6) and (339,268.6) .. (293,274.6) .. controls (247,280.6) and (260.88,236.85) .. (264,215.6) .. controls (267.13,194.35) and (231,168.6) .. (258,157.6) -- cycle ;
%Shape: Polygon Curved [id:ds4142099348862238] 
\draw  [fill={rgb, 255:red, 204; green, 153; blue, 0 }  ,fill opacity=1 ][line width=1.5]  (499,145.6) .. controls (525,136.6) and (554,187.6) .. (585,202.6) .. controls (616,217.6) and (571,275.6) .. (555,288.6) .. controls (539,301.6) and (500,302.6) .. (489,278.6) .. controls (478,254.6) and (473,154.6) .. (499,145.6) -- cycle ;
%Curve Lines [id:da3516098817239559] 
\draw    (108,191.6) .. controls (147.2,162.2) and (248.83,161.23) .. (288.64,189.81) ;
\draw [shift={(291,191.6)}, rotate = 218.66] [fill={rgb, 255:red, 0; green, 0; blue, 0 }  ][line width=0.08]  [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle    ;
%Curve Lines [id:da8949331129576243] 
\draw    (316,188.6) .. controls (355.2,159.2) and (456.83,158.23) .. (496.64,186.81) ;
\draw [shift={(499,188.6)}, rotate = 218.66] [fill={rgb, 255:red, 0; green, 0; blue, 0 }  ][line width=0.08]  [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle    ;
%Curve Lines [id:da6944762077247022] 
\draw    (95,235.6) .. controls (122,275.2) and (334,456.6) .. (551,230.6) ;
\draw [shift={(551,230.6)}, rotate = 133.84] [fill={rgb, 255:red, 0; green, 0; blue, 0 }  ][line width=0.08]  [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle    ;

% Text Node
\draw (86,199.4) node [anchor=north west][inner sep=0.75pt]  [font=\LARGE]  {$x$};
% Text Node
\draw (284,188.4) node [anchor=north west][inner sep=0.75pt]  [font=\LARGE]  {$g( x)$};
% Text Node
\draw (487,193.4) node [anchor=north west][inner sep=0.75pt]  [font=\LARGE]  {$f( g( x))$};
% Text Node
\draw (82,139.4) node [anchor=north west][inner sep=0.75pt]    {$\mathrm{Domain\ of\ } g$};
% Text Node
\draw (268,109.4) node [anchor=north west][inner sep=0.75pt]    {$ \begin{array}{l}
\mathrm{Domain\ of\ } f\\
\mathrm{or\ range\ of} \ g
\end{array}$};
% Text Node
\draw (200,142.4) node [anchor=north west][inner sep=0.75pt]  [font=\large]  {$g$};
% Text Node
\draw (417,141.4) node [anchor=north west][inner sep=0.75pt]  [font=\large]  {$f$};
% Text Node
\draw (525,132.4) node [anchor=north west][inner sep=0.75pt]    {$\mathrm{Range\ of\ } f$};
% Text Node
\draw (57,305.4) node [anchor=north west][inner sep=0.75pt]    {$\mathrm{Domain\ of\ } f( g)$};
% Text Node
\draw (251,349.4) node [anchor=north west][inner sep=0.75pt]  [font=\large]  {$ \begin{array}{l}
( f\circ g)( x) =f( g( x))\\
\mathrm{or\ } f( g)
\end{array}$};
% Text Node
\draw (488,305.4) node [anchor=north west][inner sep=0.75pt]    {$\mathrm{Range\ of\ } f( g)$};


\end{tikzpicture}

\end{document}

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