The domain of this function is not symmetrical about the origin, so the function is odd and even.
(2)4-x? ≥0,-2≤x≤2,
So x-3 < 0,
∴f(x)=√(4-x? )/(|x-3|-3)= √(4-x? )/(3-x-3)= √(4-x? )/(-x),
F(-x)= √(4-x? )/x,f(-x)=-f(x),
This function is an odd number function.
(3)f(x)= 1/(2^x- 1)+ 1/2=(2^x+ 1)/[2(2^x- 1)]
2 x- 1 ≠ 0, x≠0, the domain is symmetric about the origin.
F (-x) = (2 (-x)+1)/[2 (2 (-x)-1)] ... The numerator denominator is the same as 2 x.
=( 1+2^x)/[2( 1-2^x)]=- f(x)、
This function is an odd number function.