SOLUTION: Let f (x)=x/x-2, and g (x)=1/x-1 Find the composition (f*g)(x)=

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Question 34185: Let f (x)=x/x-2, and g (x)=1/x-1
Find the composition (f*g)(x)=
Found 2 solutions by venugopalramana, Prithwis:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Let f (x)=x/x-2,
and
LET g (x)=1/x-1=Y
Find the composition (f*g)(x)=F(G(X))=F(Y)=Y/(Y-2)
BUT Y=G(X)=1/(X-1)...SUBSTITUTING...
F(G(X))=F(Y)=Y/(Y-2)={1/(X-1)}/{1/(X-1) - 2}...MULTIPLYING THROUGH OUT WITH (X-1)
=1/{1-2(X-1)}=1/(1-2X+2)=1/(3-2X)

Answer by Prithwis(166) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=x/x-2; g(x)=1/x-1
(f*g)(x)=f(g(X))=f(1/x-1)=(1/x-1)/[(1/x-1)-2]
=(1/x-1)/[(3-2x)/(x-1)]
= 1/(3-2x)