Given f(x) and g(x) below, find and simplify (f o g)(x) and find its domain.

Question

f(x) = x/x+1

g(x) = 10/x

 

(f o g)(x) =

Answer 1

(f ο g)(x) = f(g(x)) = f(10/x) = (10/x)/[(10/x)+1]

 

                                           = (10/x)/[(10+x)/x] = 10/(10+x)

 

Domain f = {x l x≠-1}    Domain g = {x l x≠0}

 

Domain (fοg) = {x l x is in domain g and g(x) is in domain f)

 

                    = {x l x ≠ 0 and 10/x ≠ -1} = {x l x ≠ 0, -10}

 

                                                              = (-∞, -10) ∪ (-10, 0) ∪ (0,∞)