Solution: (1) This is a composite function, and its domain is the intersection of two function domains. Because a x- 1 cannot be 0, x is not equal to 0, and the domain of x 3 is that x belongs to a real number, so the domain of f(x) is that x is a real number that is not 0.

(2)f(-x)=( 1/( 1/a^x- 1)+ 1/2)(-x)^3

=(a^x/( 1-a^x)+ 1/2)(-x^3)

=(a^x+ 1)/2( 1-a^x)(-x^3)

=(a^x+ 1)/2(a^x- 1)(x^3)

f(x)=(a^x+ 1)/2(a^x- 1)(x^3)

So f(-x)=f(x), and the function f(x) is an even function.

(3) Because 0 of X 3 in x>x is greater than 0.

Therefore, x>0 (ax+1)/2 (ax-1) should be greater than 0. Because x in a > is > 0; 0 is a constant, so an x+ 1 > 0 is enough, so a> 1 > 0;

X<0 (ax+1)/2 (ax-1) should be less than 0. Because x in a > is > 0; 0 is a constant, so an x+ 1 > 0 is just an x- 1

Therefore, when a> is 1, f (x) > 0 is a constant in the definition field.