Declaring the domain of a function of two variables.

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SUMMARY

The domain of the function f(x,y) = √(4xy - 3y²) is defined by the condition 4xy - 3y² ≥ 0. This inequality ensures that the expression under the square root is non-negative, which is essential for real-valued outputs. The natural domain consists of all pairs (x,y) that satisfy this condition, confirming that the provided answer is sufficient and accurate.

PREREQUISITES
  • Understanding of functions of two variables
  • Knowledge of inequalities and their graphical representation
  • Familiarity with square root functions and their domains
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the graphical representation of inequalities in two dimensions
  • Learn about the concept of natural domains in multivariable calculus
  • Explore methods for solving inequalities involving multiple variables
  • Investigate the implications of domain restrictions on function behavior
USEFUL FOR

Students studying calculus, particularly those focusing on functions of multiple variables, as well as educators looking for examples of domain determination in mathematical functions.

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Homework Statement



I have this function of two variables:

f(x,y)=\sqrt{4xy-3y^2}

Where I have to declare the domain of the function.

Homework Equations



Since you cannot take the square root of something negative, when dealing with real numbers. The square root has to be zero or above.

The Attempt at a Solution



Well I just wanted to know if this is a sufficient answer:

D_f = \{(x,y) = 4xy-3y^2 \geq 0 \}
 
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Yes, it is. That is the "natural domain" of the given function.
 

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