We can easily see that the Domain & Range of funs. #f & g# are #RR.#
Thus, #f, g :RR rarr RR.# We denote by #R_f# & #D_f# the Range & Domain of fun. #f#, resp.
For #fog# may become defined, we must have, #R_g sub D_f,#
& similarly, for #gof#, #R_f sub D_g.# Clearly, these conds. are satisfied, we find that both #fog# & #gof# are defined, and,
#fog : RR rarr RR, gof : RR rarr RR.#
As for formula of #fog#, we have,
#fog(x)=f(g(x))=f(u),# say, where #u=g(x)#
#=8u#.......[since,#f(x)=8x]#
#=8g(x)#.....[since #u=g(x)]#
#=8(x/8)#..........[since #g(x)=x/8
#=x#
Thus, #fog : RR rarr RR,# is defined by, #fog(x)=x.#
Similarly, we can show that,
#gof : RR rarr RR,# is defined by #gof(x)=x.#
