Need some with my last problem for the night. determine the domain of tbe function (f o g)(x) where f(x) = 3x-1/x-4 and g(x) = x+1/x

We are given

f(x)=

g(x)=

\to find f o g, replace all the x in f(x) with g(x)

= Simplify by taking least common denominator and reciprocal.

Taking the least common denominator, we get

Taking reciprocal, we get

Simplifying the expression, we get

To find the domain of a composite function, we need to find the domain of f o g and the first function i.e g(x)

To find the domain of f o g, equate the denominator to 0

It means, domain is all real numbers except

Domain of g(x) is all real numbers except

combined domain is

{3 + i, 3 - i, 3, -1}

step-by-step explanation: