Question

The domain of the function f(x,y)=arcsec√x^{2}+y^{2}−2 is... Your answer: Empty Set {(x,y),x^{2}+y^{2}≥3} {(x,y),x^{2}+y^{2}≤2} R^{2} {(x,y),x^{2}+y^{2}≥2} {(x,y),2≤x^{2}+y^{2}≤3} ​

Answer 1

The domain of the function f(x,y) = arcsec√x^{2}+y^{2}−2 is the set of all (x,y) such that x^{2}+y^{2}≥2.

Step-by-step explanation:

The domain of a function represents the set of possible values that can be inputted into it. Given the function f(x,y) = arcsec√x^{2}+y^{2}−2, the domain is the set of (x,y) for which x^{2}+y^{2}≥2. This is because the square root function is undefined when its inside is less than zero, and the arcsec function is undefined when its inside is less than -1 or greater than 1. Thus, to satisfy both constraints, we need x^{2}+y^{2} to be greater than or equal to 2.

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