Defining functions that reference other values

Question

How could I define a function that references other values?

eg

a = 2 x; b = 4 k;
f[k_, x_] := a^b

Answer 1

For reasons explained here, I would strongly advise against using this kind of constructs, which in essence use global variables. However, if you must do this, here is one easy way:

ClearAll[a, b, x, k, f];
a = 2 x; b = 4 k;
f[k_, x_] =  a^b

that is, use Set instead of SetDelayed - in which case your r.h.s. will be computed at the time of the assignment.

Here is another method, which might be somewhat safer:

ClearAll[a, b, x, k, f];
a = 2 x; b = 4 k;
f[kk_, xx_] := Block[{x = xx, k = kk}, a^b]

that is, use Block to dynamically localize x and k, then call your code (a^b here).

But again, the best (safest) way is to make all functions (a and b here) explicitly take the parameters, and pass the parameters explicitly (as explained in the link I gave).