Problem: If x=ttβ11β and y=ttβ1tβ,t>0,tξ =1, a relation between x and y is:
Answer Choices:
A. yx=xy1β
B. yx1β=xy
C. yx=xy
D. xx=yy
E. none of these
Solution:
Method I.
βx=ttβ11β,y=ttβ11β=t1+tβ11β=tβ
ttβ11ββ΄y=tx. Also y=t(tβ11β)t=xtyx=(xt)x=xtxβ΄yx=xy.β
Method II. x=ttβ11β,y=ttβ1tββ΄xyβ=ttβ1tββ
tβ11β=tβ΄x=(xyβ)y/xβ11β=(xyβ)xβyxβ
β΄xyβx=xxyxββ΄xy=yx