Question

Domains of functions of three or more variables 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). $$p(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}-9}$$

   Domains of functions of three or more variables 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).
$$p(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}-9}$$

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 13, Problem 48

Instant Answer

Solved by Expert Linh Vu

08/31/2020

Step 1

The square root function is only defined for non-negative numbers, so we need to find the values of $x$, $y$, and $z$ for which $x^{2}+y^{2}+z^{2}-9 \geq 0$. Show more…

Show all steps

Thanks for your feedback!

Domains of functions of three or more variables 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). $$p(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}-9}$$

Play audio

Feedback

Linh Vu and 84 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Domain of a Multivariable Function

The domain of a function of several variables is the set of all input points in the relevant space (such as R^3 for functions of three variables) where the function is defined. In determining this set, one must account for restrictions imposed by operations like division, taking roots, or logarithms, ensuring that every operation yields a real number under consideration of the function's definition.

Radical Function Constraints

When dealing with functions involving square roots or other even roots, the expression inside the radical (the radicand) must be non-negative to produce real-valued outputs. This requirement leads to setting up an inequality where the radicand is greater than or equal to zero, which can often result in geometric descriptions in multiple dimensions such as regions defined by spheres.

Please give Ace some feedback