Enumarate and combine functions?

Questions
1

How do you enumerate functions?
Can i just enumarte them like that:

f1[x[1],x[2],...]=...
f2[x[1],x[2],...]=...

and how do I combine the functions afterwards?
I tried it this way, but didnt work:

L[x[1],x[2],...]=f1[x[1],x[2],...]*f2[x[1],x[2],...]...

is this the right way, somehow I’m getting wrong results.
Thank you!

2

I would do it like this:

f1[x1_, x2_] := x1*x2;
f2[x1_, x2_] := x1 + x2;
L[x1_, x2_] := f1[x1, x2]*f2[x1, x2]
3

I tried this, but Mathematica still doesn’t output the resulting function.
But when I input values it puts out the correct result.

L[1,2]=6

But how can I make Mathematica output the resulting function?

4

I don’t quite understand what you expect as an output. Maybe this:

In[166]:= f1[x1_, x2_] := x1*x2;
f2[x1_, x2_] := x1 + x2;
L[x1_, x2_] := f1[x1, x2]*f2[x1, x2];
L[x1, x2]

Out[169]= x1 x2 (x1 + x2)

You can also try ?L to see the formula associated with the function L.