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Calculus Level 5

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.

If you are looking for more such simple but twisted questions, Twisted problems for JEE aspirants is for you!
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