(*Q1(a).*)
(*f[x_]:=\[LeftBracketingBar]x-2\[RightBracketingBar]-1;*)
f[x_]:=Abs[x-2]-1;
(*Plot[f[x],{x,-4,6},AxesLabel->{x,y}];*)
fs1[x_]:=f[xdum]/.{xdum->x+1};
(*Plot[{f[x]},{x,-4,6}]*)
fs2[x_]:=fs1[2x];
fs3[x_]:=-fs2[x];
Plot[{f[x],fs1[x],fs2[x],fs3[x]},{x,-4,6},AxesLabel->{x,y}]
Print["f_1(x)=",fs3[x]]

(*Q1(b).
Plot on a new graph cot⁡x for x∈[-2π,2π].Label clearly the values at which the function intersects with the x-axis
*)
y[x_]:=Cot[x];
Plot[y[x],{x,-2Pi,2Pi},AxesLabel->{x,y},PlotLabel->"cot x"]

Integrate[Sqrt[y]/(y-1),y]

Integrate[Log[y-1]/Sqrt[y],y]

Integrate[Log[y],y]