f(x) = 2/3x-1

g(x) = x+4/x

(g o f)(x) = ?
x does not equal 1/3

Can someone explain how to do this one?

replace the x with the function.

g of (f(x))

2/(3(x+4/x) -1

I am not sure the g(x) is (x+4)/x or is is x plus 4/x

that matters when simplifying.

Assuming the usual carelessness with parentheses, I guess you have

f(x) = 2/(3x-1)
g(x) = (x+4)/x

g(f) = (f+4)/f
= (2/(3x-1)+4)/(2/(3x-1))
= 6x-1

To find the composition of functions (g o f)(x), you need to substitute the function f(x) into the function g(x), which means replacing x in g(x) with f(x). In this case, we have:

f(x) = 2/3x - 1
g(x) = (x + 4) / x

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Substitute f(x) into g(x):
(g o f)(x) = g(2/3x - 1)

Now, replace the x in g(x) with 2/3x - 1:
(g o f)(x) = ((2/3x - 1) + 4) / (2/3x - 1)

Simplify this expression further if possible. However, note that there's a restriction mentioned: x ≠ 1/3. This means that any value of x equal to 1/3 would yield an undefined result in the final expression.

Keep in mind that there might be additional simplifications or restrictions that could arise during the process of working with this particular composition of functions.