∵g(x) and f(x) are symmetric about y =x ∴g(x) is the inverse function of f(x).

It is known that g(x)=log( 1/2)(x) is the logarithm of x with 1/2 as the base.

∴g(x^2)=log( 1/2)(x^2)

For the function y = log (1/2) (x 2), because the function values of x and -x are equal, it can be seen that it is an even function.

The composite function satisfies "the same increase but different decrease". Similarity and dissimilarity refer to the similarities and differences of monotonicity.

For y = log (1/2) (u), u = x 2.

X<0, u = x 2 decreases, u >；; 0, when y=log( 1/2)(u) decreases.

Monotonicity is the same, so the composite function is in X.