Mathematica beginner question: Function nesting

[physicsan]

Hello,
I'm quite new to Mathematica and stuck at a point, where I have searched for hours to find a solution, but there seems no way out.

Let's say we have two functions,
f1[x_,y_]=x+y
f2[x_,y_]=x*y

How can a build a function f3, which is e.g. the sum of the other functions f1 and f2, i.e. f3[x_, y_]=x+y+x*y, but without copy&paste, but with direct dependency on f1 and f2?

With f3=f1[x,y]+f2[x,y], the functional dependency on x and y is missing. I need a f3, which also has the same input arguments as f1 and f2 (namely x and y).
With f3[x_,y_]==f1[x,y]+f2[x,y] the functional dependency on the parameters is also not working.

Thanks you for your help,
I'm really desperate :(

 

[phyzguy]

I think that you don't understand the difference between =(immediate assignment), :=(delayed assignment) and == (test for equality). You want to use := in function assignments so that the assignment is not made until you request evaluation. Try the attached notebook - I think it does what you want.

 

[physicsan]

Hi,

a thousand thanks! This is exactly what I was looking for! Sorry for my dummy question, it really seems so dummy now :s
Thank you again for your profound and amazingly fast help, you really made my day! :)

 

[phyzguy]

You're welcome. Glad I could help.