0
$\begingroup$

I found this question interesting:

Which one of the following functions are equal to $f(x)=\lfloor \sqrt{x}-\lfloor \sqrt{x}\rfloor\rfloor$? ($\lfloor \cdot \rfloor$ is the floor function)

  1. $g(x)=\sqrt{x-|x|}$
  2. $g(x)=\sqrt{-x+|x|}$
  3. $g(x)=\sqrt{x+|x|}$
  4. $g(x)=\sqrt{-x-|x|}$

What I have done is to examine the domains of above functions regarding the fact that $0\leq x-\lfloor x\rfloor<1$. Just to share your ideas about this Maths multiple choices. Thanks.

1 Answers 1

2

Think that $f(x)$ is the floor function of the decimal part of $\sqrt{x}$ so it is identically zero in for all $x\geq 0$. Which of the functions $g(x)$ is identically zero for all $x\geq 0$?

  • 3
    (+1): That isn't quite enough on its own, as it leaves two options. Only one of them shares the same domain of definition, though.2012-10-30