Math Problem Statement
What is the domain of the function g(x) = 3 / √(x² - 16)?
Solution
The given function is:
Domain of the Function
To determine the domain of , we must identify the values of for which the function is defined.
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The square root, , must be defined. This implies: Simplifying this inequality: Therefore, or .
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Additionally, the denominator must not be zero, so: This implies:
Thus, the domain of the function is:
Would you like further details or have any questions?
Here are some related questions for further exploration:
- What is the range of the function ?
- How would the graph of look?
- Can we find the vertical asymptotes of this function?
- How can we differentiate ?
- What happens to as ?
Tip: Always check for restrictions in the domain when square roots or denominators are involved in a function.
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Square Roots
Formulas
g(x) = 3 / √(x² - 16)
Theorems
Domain restrictions
Square root function properties
Suitable Grade Level
Grades 10-12