Let f  be the greatest integer function and g be the modulus

∵ f(x)=[x],[.]   denotes the greatest integer function and g(x)=|x| Now , (fog)x=f(g(x))=f(|x|)=[|x|] And    (gof)x=g(f(x))=g([x])=|[x]| Option (a): (gof−fog)(−53) =|[−53]|−[|−53|] =|−2|−[53]=2−1=1 Option (b): (f+2g)(−1)=f(−1)+2g(−1)                       =[−1]+2|−1|                       =−1+2=1 Option(c): (gof−fog)(53)=(gof)(53)−(fog)(53)                                =|[53]|−[|53|]                               =|1|−[53]=1−1=0 Option(d):                  (f+2g)(1)=f(1)+2g(1)=[1]+2|1|=1+2=3