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

54

step-by-step explanation:

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^