order of evaluation defining a function

Question

I'm quite sure this is an easy question but Im missing something.

I wish to define a function whose action depends on whether the input is a single matrix or a multiplication of two, For example:

I would want to do get:

f[x*y]
(* x+y *)

f[x]
(* x *)

Even though this example isn't interesting it is enough to demonstrate my issue.

I tried:

f[x_] := If[Head[Unevaluated[x]] == Times, 
(Unevaluated[x][[1]]) + (Unevaluated[x][[2]])
,
x]

Indeed I get:

f[x*y]==x+y
(* True*)

But I get:

f[x]
(* If[Symbol == Times, Unevaluated[x][[1]] + Unevaluated[x][[2]], x] *)
f[7]
(* If[Integer == Times, Unevaluated[7][[1]] + Unevaluated[7][[2]], 7] *)

Any explanation or an explanation of a better way to achieve my goal are welcome

Answer 1

Note

This answer explains why the problem in the question happens and how to solve it without changing the approach. Alucard's answer shows how to solve the problem with a more "Mathematica like" approach using SetDelayed with different patterns.

Original answer

A bit of an explanation of what I already said in the comments:

If you look at the output for f[x], you'll see that Symbol == Times has not been replaced by False. For this reason, the If expression is returned unevaluated.

This happens because Symbol andTimes don't have a value (although they are "known" symbols, they're treated as unknown variables for the sake of comparison since there are no OwnValues).

To always get either True or False, you can use SameQ (=== for short):

In[1]:=  Symbol === Times
Out[1]:= False

Answer 2

you can use pattern matching

f[x_*y_] := x+y
f[x_] := x

examples:

f[2*3]
f[x]
f[x*y]
f[5]

gives you

 5
 x
x + y
 5