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.

 

[alphy]

I understand your frustration and the importance of finding efficient solutions to problems. In this case, the solution lies in using the concept of function composition. This means that you can create a new function, let's call it f3, by nesting f1 and f2 within each other. In Mathematica, this can be done using the Composition function.

For example, you can define f3 as follows:

f3[x_,y_]:=Composition[f1,f2][x,y]

This will create a new function f3 that takes in the same input arguments as f1 and f2, and returns the sum of their outputs. You can then use f3[x,y] to get the desired result.

I hope this helps and good luck with your future Mathematica endeavors!