The Functions F And G Are Defined For All X R 1 0 1 By F X X 1 1 X And G X 1 X

General approach is to transform both sides of the equality until they start appearing similar.

Consider the right hand side, we have:

##(f@g)(x) = f(g(x)) = (1/x +1)/(1-1/x) = (x+1)/(x-1)##

(defined since ##x=1## is not in the defined interval) (1)

Consider the left hand side, we let: ##(f@g)^-1(x) = y## where ##(f@g)(y) = x##

(according to definition of inverse function) From that, we can have : ##(f@g)(y) = (y+1)/(y-1) = x####xy – x = y + 1 ####y = (x+1)/(x-1)##= ##(f@g) ^-1 (x) ##

(defined since x = 1 is not included in the defined interval) (2)Thus, from (1) & (2), Q.E.D

Prof. Angela

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