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How do you find the compositions given #f(x) = x/(x + 1)#, #g(x) = x^2 - 1#?

1 Answer

Konstantinos Michailidis

Jan 25, 2016

For f(x) the domain is #R-{1}# and for g(x) is #R# where #R# is the set of real numbers.
Hence

#f(g(x))=(x^2-1)/(x^2-1+1)=(x^2-1)/(x^2)=1-1/(x^2)#

and

#g(f(x))=(x/(x+1))^2-1#

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