If \(f(x)\) and \(g(x)\) are functions defined in the real domain and co-domain, such that \(\sqrt{1-(f(x))^2}=g(x)\), which of the following statements are necessarily true?

**A:**If \(g(x)\) is periodic with period 1, \(f(x)\) is periodic with period \(\dfrac{1}{2}\)**B:**If \(g(x)\) is a continuous function, \(f(x)\) is also continuous in their respective domains.**C:**If \(-f(c)=f'(c)=0.5;\dfrac{g'(c)}{g(c)}=\dfrac{1}{3}\).**D:**If \(g(x)\) is an even function,\(f(x)\) is odd.**E:**If \(g(x)\) is an odd function, \(f(1024)\) is of unit modulus.

×

Problem Loading...

Note Loading...

Set Loading...