# CAT 2000 | Question: 76

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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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