Question

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?

Answer 1

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.

Answer 2

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