input courbes;
beginfig(1);
repere(10cm,10cm,4cm,4cm,1cm,1cm);
trace.axes(1pt);
marque.unites(1mm);
draw rpoint(r_xmin,-r_xmin+1)--rpoint(r_xmax,-r_xmax+1);
draw rpoint(r_xmin,1)--rpoint(r_xmax,1);
vardef fx(expr t) = t enddef;
vardef fy(expr t) = -t/2+1+sqrt(t**2+1)/2 enddef;
path courbe;
courbe = ftrace(r_xmin,r_xmax,100) en_place;
draw courbe withpen pencircle scaled 1.5pt withcolor red;
draw (courbe reflectedabout (origine,rpoint(1,1)))
     withpen pencircle scaled 1.5pt
     withcolor (1,0,1);
decoupe.repere;
etiquette.axes;
etiquette.unites;
label.top(btex $y=f(x)$ etex scaled 1.5,rpoint(r_xmax-2,1.2)) withcolor red;
label.rt(btex $y=f^{-1}(x)$ etex scaled 1.5,rpoint(1.3,r_ymax-1)) withcolor (1,0,1);
label.ulft(btex $y=-x+1$ etex, rpoint(-1.5,2.5));
label.bot(btex $y=1$ etex, rpoint(-1.5,1));
endfig;
end