I am confused by the following problem. (Please also find attachment)

Given X is a random variable, g is a real function of X mapped from R to R.

(g:X=>R:R)

(a) Find E[g(X)/X] (Find the expectation of E[g(X)/X] given X

(b) Find Var(g(X)/X]

Usually, we are only asked to find conditional expectation of g(X) given a different random variable such as Y.

For E[g(X)/X], I can only expand it as follow:

E[g(X)/X] =

∫g(x)P(g(x)/X=x)dx = ∫g(x) P(g(x),X=x)/P(X=x)dx

For Var(g(X)/X), it can be found using the general formula:

Var(X) = E(X^2)-(E[X])^2

Please help and give me some advice. Thanks!