Let f  be a function satisfying f(x+y)+6−f(y)=f(x)f(y)  and f(h)→6  as h→0. Then

R.H.L=limx→x+f(x)=limh→0f(x+h)              =limh→0f(x)f(h)−6−f(h)           =f(x)limh→0f(h)−limh→06−f(h)=f(x) . 6−0=6f(x)≠f(x)This shows that if f(x)≠0, then f is discontinuous atx.  iff(x)=0,  then f(x) is continuous atx.