Assuming x and y are the same size, that all the functions involved are vectorized and in scope:
function z = h(x, y)
fxy = f(x, y);
gxy = g(x, y);
z = NaN(size(x));
condition1 = fxy <= gxy;
z(condition1) = h1(x(condition1), y(condition1));
z(~condition1) = h2(x(~condition1), y(~condition1));
If you've define f, g, h1, and h2 as anonymous functions in the workspace from which you're calling h, you should pass them into h as input.
function z = h(x, y, f, g, h1, h2)
