X1,X2, ….Xn are iid random variables. Can I say that 1/X1 , 1/X2,... , 1/Xn are independent.

I referred to a theorem on this in a literature, it says if X,Y are independent then f(X) and g(X) are independent given that function f,g are borel measurable function. now the question to me can i say f(x)=1/x is a borel measurable function.

Any thoughts on this would be highly appreciated

Thanks