Chapter 12: Q 28. (page 916)

In Exercise, evaluate the given function at the specified points in the domain, and then find the domain and range of the function.
$f (x, y, z) = \frac{x + y + z}{x y z}, (1, - 2, 6), (- 3, - 2, 4)$

Short Answer

Expert verified

$\begin{array}{rcl} f (1, - 2, 6) & = & - \frac{5}{12} \\ f (- 3, - 2, 4) & = & - \frac{1}{24} \end{array}$

Domain is $R^{3} - \{(0, y, z), (x, 0, z), (x, y, 0)\}$ and range is R.

Step by step solution

Step 1. Given information

Function is $f (x, y, z) = \frac{x + y + z}{x y z}$

Step 2. Explanation

$\begin{array}{rcl} f (1, - 2, 6) & = & \frac{(1) + (- 2) + (6)}{(1) (- 2) (6)} \\ = & \frac{5}{- 12} \\ = & - \frac{5}{12} \\ f (- 3, - 2, 4) & = & \frac{(- 3) + (- 2) + (4)}{(- 3) (- 2) (4)} \\ = & \frac{- 1}{24} \\ = & - \frac{1}{24} \end{array}$

For domain:

width="52">xyz=0

x= 0 or y = 0 or z = 0

These points are to be excluded from function's domain.

So, domain is $R^{3} - \{(0, y, z), (x, 0, z), (x, y, 0)\}$ range is R.

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In Exercise, evaluate the given function at the specified points in the domain, and then find the domain and range of the function.
$f (x, y, z) = \frac{x + y + z}{x y z}, (1, - 2, 6), (- 3, - 2, 4)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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In Exercise, evaluate the given function at the specified points in the domain, and then find the domain and range of the function.fx,y,z=x+y+zxyz,1,-2,6,-3,-2,4

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Calculus

Geometry

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Pure Maths

Study anywhere. Anytime. Across all devices.

In Exercise, evaluate the given function at the specified points in the domain, and then find the domain and range of the function.
$f (x, y, z) = \frac{x + y + z}{x y z}, (1, - 2, 6), (- 3, - 2, 4)$