Exploring the Domain and Range of a Multivariable Function

In summary, we discussed the function f(x,y) = ln(y-2x) and its largest possible domain, range, and domain for which the function is greater than 0. We also explained why two different level curves cannot intersect due to the definition of a function.
  • #1
Saunderssim
2
0
Hi,

Kinda need help for this question.

f(x,y) = ln(y-2x)

1. Find the largest possible domain
2. Find the range of the function where the function is defined over the largest possible domain
3. find the largest possible domain if it is desired that f(x,y) > 0

Explain why two different level curves cannot intersect.
 
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  • #2
Saunderssim said:
Hi,

Kinda need help for this question.

f(x,y) = ln(y-2x)

1. Find the largest possible domain
What is the largest possible domain of ln(x)?

2. Find the range of the function where the function is defined over the largest possible domain
What is the range of ln(x)?

3. find the largest possible domain if it is desired that f(x,y) > 0
For what values of x is ln(x)> 0?

Explain why two different level curves cannot intersect.
What is the defintion of "level curves"? What would be true about a point at which two different level curves intersect? How does that contradict the definition of "function"?
 
  • #3
domain: x>0
Range: (-infinity, infinity)
value: x>1

I don't quite know how to answer the last part of the question. Well a function mostly has one specific answer for every specific value...
 

1. What is a multivariable function?

A multivariable function is a mathematical function that involves more than one independent variable. This means that the output of the function is dependent on multiple input variables.

2. How is a multivariable function different from a single variable function?

A single variable function has only one independent variable, while a multivariable function has more than one. This makes multivariable functions more complex and allows them to represent relationships between multiple variables.

3. What are some common examples of multivariable functions?

Examples of multivariable functions include the distance formula, which has two independent variables (x and y coordinates), and the volume of a cylinder, which has three independent variables (radius, height, and pi).

4. What is the purpose of studying multivariable functions?

Studying multivariable functions allows us to understand and model relationships between multiple variables in various fields such as physics, economics, and engineering. It also helps in solving real-world problems and making predictions.

5. What are some techniques used to analyze multivariable functions?

Some techniques used to analyze multivariable functions include partial derivatives, critical points, and optimization methods. These techniques allow us to find maximum and minimum values, determine rates of change, and identify points of interest on the function's graph.

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