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Instructions
Directions for the next 2 questions:
For real numbers x, y, let
f(x, y) = Positive square-root of (x + y), if $$(x + y)^{0.5}$$ is real
f(x, y) = $$(x + y)^2$$; otherwise
g(x, y) = $$(x + y)^2$$, if $$\sqrt{(x + y)}$$ is real
g(x, y) = $$- (x + y)$$ otherwise
Question 114
Under which of the following conditions is f(x, y) necessarily greater than g(x, y)?
Solution
When both x and y are less than -1, g(x,y) > 2 and f(x,y) > 4 and $$f(x,y) = g(x,y)^2$$
So, f(x,y) > g(x,y)
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