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

each side has a different length.  

step-by-step explanation:

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !