Answer
The function is odd and has symmetry with respect to the origin.
Work Step by Step
f(x)=2x$\sqrt {1-x^2}$
f(-x)=2(-x)$\sqrt {1-(-x)^2}$
f(-x)=-2x$\sqrt {1-x^2}$
-f(x)=-(2x$\sqrt {1-x^2}$)
-f(x)=-2x$\sqrt {1-x^2}$
Since f(-x)=-f(x), the function is odd. Odd functions have symmetry with respect to the origin.