Question

I have trouble with these questions.
If f(x) = 1 / (x + 4) and g(x) = 8 / (x - 1) find the domain of f(g(x). I found All reals except x = -1 but correct is All reals except x = 1 and x = -1. Can someone explain why this is?

Answer 1

domain is also defined by g(x) function.
so if the composition is \[g(\color{Red}{f(x)})\] you have to find the domain of g(f(x)) and f(x)

Answer 2

domain is also defined by g(x) function.
so if the composition is \[g(\color{Red}{f(x)})\] you have to find the domain of g(f(x)) `and ` f(x)

Answer 3

Ah Ok I see .Thank you.