Math Problem Statement
Solution
The task here involves determining whether the function is defined at specific points given in the options.
For the function to be defined at a point , the expression inside the square root, , must be non-negative. Specifically, we need:
or equivalently,
Now, we will check each point given in the options to see if it satisfies this inequality.
Checking Each Option
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Option a) :
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Option b) :
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Option c) :
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Option d) :
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Option e) :
Conclusion
The function is defined at points b), c), d), and e). Only option a) does not satisfy the inequality. Therefore, the correct answers would be b, c, d, and e.
Would you like further details or have any specific questions?
Here are some related questions to expand on this topic:
- How can inequalities involving multiple variables be visualized on a graph?
- What happens to the function if the inequality becomes an equality?
- How do different values in the function affect the domain constraints?
- Can similar methods be used to determine the domain of more complex functions?
- What are some practical applications of defining functions with restricted domains?
Tip: When analyzing inequalities involving functions, always simplify the expression to make the conditions for the function's domain more apparent.
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Inequalities
Function Domains
Formulas
f(x, y) = 1 / sqrt(-y^2 - 5 * x^2 + 166)
Inequality condition: -y^2 - 5 * x^2 + 166 >= 0
Theorems
Domain of a function with a square root in the denominator
Suitable Grade Level
Grades 11-12