SOLUTION: Find the domain of the composite function f o g f(x)=1/x-9;g(x)=1/x According to the rules If there are restrictions on the domain of both f and g, then we apply the restrict

Question 775582: Find the domain of the composite function f o g
f(x)=1/x-9;g(x)=1/x
According to the rules If there are restrictions on the domain of both f and g, then we apply the restrictions on f to the function g and keep the restrictions on g to find the domain of f o g. If we apply this restriction of f to the g, then g(x)=1/x ≠9 or x ≠ 1/9. Now apply this and the restriction on g to the composite function and submit the domain.
Thank you,
Romy
Answer by tanjo3(60) (Show Source): You can put this solution on YOUR website!
(1) f ∘ g represents f(g(x)) so let us first substitute g(x) in f(x):
f ∘ g = [1/(1/x)] - 9
(2) Simplify the function. (1 � (1/x) = 1 � x = x)
f ∘ g = x - 9
(3) The function is linear therefore it's domain is R (all real numbers).
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