Select ALL statements that are FALSE about the domain and range of f(x. y, z) =

Question

Select ALL statements that are FALSE about the domain and range of f(x. y, z) = ln(16 - 4x2 - 4y2 - z2). The domain is The domain is The range is all positive real numbers. The range is all real numbers.

Explanation / Answer

(a) and (c) are wrong (a) the domain is defined only for ln f(x) > 0 (Note that it is strictly bigger than 0 because, ln 0 is undefined, hence, a is wrong because it allows for the case that f(x) = 0 and includes it into its domain (c) the range of the function is all possible values of the ln x function which spans (to infinity) both positive and negative numbers, thus selecting only the positive numbers is wrong for the range

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