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A function is given implicitly by 2^(|x| + |y|) + 2^(|x| - |y|) = 2. Which of the following is true?

1. Domain of the function is a singleton
2. Range of the function is a singleton
3. the graph of the function meets the line y = x
4. the maximum value of the function is 2

Correct answer: Domain of the function is a singleton

Solution

Since 2^|x| >= 1 and 2^|y| + 2^(-|y|) >= 2, their product is at least 2, with equality only when both are minimal, i.e. x = 0 and y = 0. So the only solution is the single point (0,0).

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