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Chapter 12: Problem 46

Find the domain of the following functions. If possible, give a description of the domains (for example, all points outside a sphere of radius 1 centered at the origin). $$f(x, y, z)=2 x y z-3 x z+4 y z$$

Short Answer

Expert verified
Answer: The domain of the given function is the entire 3D space, which can be written as \((x, y, z) \in \mathbb{R}^3\).

Step by step solution

01

Identify the function type

The given function is a polynomial in three variables: $$f(x, y, z)=2xyz - 3xz + 4yz$$
02

Check for any restrictions on the variables

Polynomial functions do not impose any restrictions on their variables. Therefore, there are no restrictions on the variables x, y, and z in this case.
03

Identify the domain

Since there are no restrictions on the variables, the domain of the function is the entire 3D space. We can write this domain as follows: Domain of f: \((x, y, z) \in \mathbb{R}^3\)
04

Describe the domain (if possible)

We cannot provide a geometric description of the domain in this case, as the entire 3D space includes all the points in every possible direction.

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Most popular questions from this chapter

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