Math Forum / Math Software / Mathematica / February 2010

There are several ways to achieve what you want. The smallest
change to your code needed to obtain the desired result would be
to define the functions as:

f[x_]=a x^2;
g[a_,x_}= 2 a + f[x];

But, usually (not always) it is better to use SetDelayed (:=)
rather than Set (=) so that evaluate occurs when the function is
used rather than when it is defined. That would be done as follows:

f[x_]:= a x^2
g[a_, x_]= 2 a + f[x];

Note, I've used Set not SetDelayed in the definition of g. Since
f is defined in terms of a single argument x, it is necessary to
evaluate f[x] when defining g. Otherwise, f will not see the
value of a provided to g.

While the above works, I would do the following:

f[x_, a_]:= a x^2
g[x_, a_]:= 2 a f[x, a]

This causes evaluation to occur when g is evaluated and makes
both f and g depend on arguments passed to them. Making
functions depend on things not directly passed to them often
causes unexpected results when the function is used elsewhere in
a notebook. And this kind of problem can be difficult to find.