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Consider a function from N to N and G from N to N and H from N to R,defined as F(x)=2x G(y)=3y+4,H(z)=sin z For every x,y,z element of N show that Ho(GoF)=(Hog)oF {h of gof=(hog)oF

gof =g(2x)
       =3(2x)+4
       =6x+4
ho(gof) =sin(6x+4)  ........(i)

hog = h(g(y)

       =h(3y+4)
       =sin (3y+4)
(hog)of =sin(3*2x + 4)
            =sin(6x+4)  ..........(ii)

from (i) and (ii),

  ho(gof) =   (hog)of


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