Suppose I Know That Holly Always Has a Certainty Equivalent $\left(x_{C E}\right)$

Multiple Choice

Suppose I know that Holly always has a certainty equivalent $\left(x_{C E}\right)$ equal to 0 . Which of the following utility functions describes Holly's preferences?

A) $\mathrm{U}(\mathrm{x}) =\ln (\mathrm{x})$
B) $\mathrm{U}(\mathrm{x}) =\mathrm{x}$
C) $\mathrm{U}(\mathrm{x}) =\mathrm{x}$ if $\mathrm{x}>0$ and $\mathrm{U}(\mathrm{x}) =-2 \mathrm{x}$ if $\mathrm{x}<=0$
D) $U(x) =\sqrt{x}$