F(x) = (x+1)/x f o g (x) = x, what is g(x) ??

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Answer 1 · 2018-05-22T01:02:30

#g(x)=1/(x-1)#

#f(x)=(x+1)/x#

#f(g(x))=x#

Our first step is to plug #g(x)# into #f(x)#.

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

Now, we know that this equals #x#.

#x=(g(x)+1)/(g(x)#

In order to solve for #g(x),# we must isolate it. We can start simplifying because #g(x)/g(x)=1#.

#x=1+1/g(x)#

#x-1=1/g(x)#

#g(x)=1/(x-1)#