Problem 3
Question
What is the domain of \(g(x, y)=1 /(x y) ?\)
Step-by-Step Solution
Verified Answer
Answer: The domain of the function g(x, y) = 1/(x*y) is the set of all ordered pairs (x, y) such that \(x \neq 0\) and \(y \neq 0\), which can be written as \(D={(x, y) | x \neq 0, y \neq 0}\).
1Step 1: Write down the given function
The given function is g(x, y) = 1/(x*y).
2Step 2: Determine when the function is undefined
The function will be undefined when the denominator of the fraction is equal to zero. The denominator of the fraction is x*y. So, we need to find when x*y = 0.
3Step 3: Solve for x and y
The equation x*y = 0 is satisfied when either x = 0 or y = 0.
4Step 4: Describe the domain of the function
The function is defined for all values of x and y except when x = 0 or y = 0. Therefore, the domain of the function is given by the set of all ordered pairs (x, y) such that \(x \neq 0\) and \(y \neq 0\), which can be written as \(D={(x, y) | x \neq 0, y \neq 0}\).
Other exercises in this chapter
Problem 3
Where does the plane \(-2 x-3 y+4 z=12\) intersect the coordinate axes?
View solution Problem 3
Suppose \(w\) is a function of \(x, y,\) and \(z,\) which are each functions of t. Explain how to find \(\frac{d w}{d t}\).
View solution Problem 3
Find \(f_{x}\) and \(f_{y}\) when \(f(x, y)=x \cos (x y).\)
View solution Problem 4
If \(f_{x}(a, b)=f_{y}(a, b)=0,\) does it follow that \(f\) has a local maximum or local minimum at \((a, b) ?\) Explain.
View solution