What is xf compared to fx How are they different?

Answer 1

If x and f are quantities then xf and fx are the same if they belong to a commutative space. If not, they normally do not. Multiplication of matrices, for example is cont commutative. In fact, it is quite possible that xf has a value but fx does not even exist.

if x and f are functions then again, fx and xf will not generally be the same.

For example suppose x = "add 5 to it" and f = "square it".

Then xf(3) = x(9) = 14

while fx(3) = f(8) = 64