The x power of a is represented by a x, and the -x power of a is represented by a (-x).

y=f(x)=[a^x+a^(-x)]/2

y=f(-x)=[a^(-x)+a^(x)]/2=f(x)

So y = f (x) = [a x+a (-x)]/2 is an even function.

Parity function judgment rule

The domain of y=f(x) is symmetric about the origin.

(1) If f(x)+f(-x)=0, then f(x) is odd function.

(2) If f(x)=f(-x), then f(x) is an even function.