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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