I would like to draw in TeX the following, but I'm pretty new at tikz therefore I have no clue.
I would like to give the geometrical interpretation of the domain and the range of a composite function. How do I do that?
Thank you in advance. Any help would be appreciated.
Drawing done with Mathcha: 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}
