Let # f(x) = 3/(x-1)# and #g(x) = 2/x#, how do you find each of the compositions?

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Answer 1 · 2016-01-06T15:04:45

# f(g(x)) = (3x)/(2 - x ) #

# g(f(x)) =( 2(x - 1 ))/3 #

(a) # f(g(x)) = f ( 2/x )#

now substitute # 2/x #in for x in f(x)

# rArr f (2/x) = 3/((2/x) - 1) #

can tidy this up by multiplying numerator and denominator by x.

#rArr 3/((2/x) -1 ) = (3x)/(2 - x ) #

(b) # g(f(x)) = g ( 3/(x - 1)) #

now substitute # 3/ (x - 1 ) # in for x in g(x)

# rArr g (3/(x - 1 )) = 2/(3/((x - 1 )) #

now tidy up

# rArr g(f(x)) =( 2(x - 1 ))/3 #