Given f(x) = 1/x^2 -4 and g(x)= log, identify the steps you would take to determine the domain of (g ° f) (x). What is the domain of (g ° f) (x)?

Question

Would the domain of (f ° g) (x) be the same ? Explain the domain of (f°g) (x)

Answer 1

(f◦g)(x) = f(g(x)) = 1/(g^2-4) = 1/((logx)^2 - 4)
logx requires that x>0
Since the denominator cannot be zero, |logx|>2, so x<1/e^2 or x>e^2

(g◦f) = g(f) = log(1/(x^2-4))
so |x|≠2 and |x|>2

so, what do you think?