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June 21st, 2019, 05:18 PM   #1
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find range of the function

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June 22nd, 2019, 10:46 AM   #2
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Is y a constant, or is the function f(x,y)?

Either way, "Find the range," can be treated as, "Find the minima/maxima."
Find df/dx and df/dy (if a 2-D function) and set them equal to zero.

To simplify it, we can tell that both the minimum and maximum will be at sin^2y = 1 if y is variable. We also know that the range will definitely be smaller than +/-(1+sqrt(2)), so you can check your answer against that.

Also, you can plot f(x,y) over [-pi,pi]x[-pi,pi] to check your answer. (Or just f(x,pi) for -pi <= x <= pi, using the observation above.)
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