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Answer the following question based on the information given below.
For real numbers $x, y,$ let

$f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\;\text{if}\; (x + y)^{0.5}\;\text{is real} \\  (x + y)^2,\;\text{otherwise} \end{matrix}\right.$
$g(x, y) = \left\{\begin{matrix} (x + y)^2,\;\text{if}\; (x + y)^{0.5}\;\text{is real} \\  –(x + y),\;\text{otherwise} \end{matrix}\right.$

Under which of the following conditions is $f(x, y)$ necessarily greater than $g(x, y)?$

  1. Both $x$ and $y$ are less than $–1$
  2. Both $x$ and $y$ are positive
  3. Both $x$ and $y$ are negative
  4. $y > x$
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