Given f(x)=1/x^2 -4 and g(x)=log(x) identify the steps you would take to determine the domain of (g ∘ f)(x). What is the domain of (g ∘ f)(x)?
2 answers
b) Would the domain of (f ∘ g)(x) be the same? Explain. What is the domain of (f ∘ g)(x)?
I assume you mean
f(x) = 1/(x^2-4)
If so, then
(g ∘ f)(x) = g(f) = log(f) = log(1/(x^2-4)) = -log(x^2-4)
so, the domain of g is where f > 0; that is, where |x| > 2
(f ∘ g)(x) = f(g) = 1/((logx)^2-4)
So now we need x>0 and logx≠2
f(x) = 1/(x^2-4)
If so, then
(g ∘ f)(x) = g(f) = log(f) = log(1/(x^2-4)) = -log(x^2-4)
so, the domain of g is where f > 0; that is, where |x| > 2
(f ∘ g)(x) = f(g) = 1/((logx)^2-4)
So now we need x>0 and logx≠2