if f(x)=1/(x-2) and g(x)=4/x, what is (f*g)(x)?

The functions given are f(x) = 1/(x - 2) and g(x) =
4/x.

(f*g)(x) = fog(x)  =
f(g(x)).

To find f(g(x)), first we find g(x). g(x) =
4/x.

Substituting this in
f(x)

=>
f((4/x))

=> 1/ ((4/x) -
2)

=> 1 / [(4 -
2x)/x]

=> x / (4 -
2x)

Therefore the required result is x / (4 -
2x)