Math Problem Statement
Solution
To find the domain of the function , we need to determine when the function is defined. There are two primary considerations:
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The square root condition: The expression under the square root, , must be non-negative (i.e., ) because square roots of negative numbers are undefined in the real number system. This gives:
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The denominator condition: The denominator must not be equal to zero because division by zero is undefined. Therefore, we need:
Combining these conditions:
- From the square root condition, .
- From the denominator, and .
Thus, the domain of the function is , but excluding .
Domain in interval notation:
Would you like further details or clarifications on any steps?
Here are some related questions to consider:
- What if the square root were of a different expression?
- How does adding other restrictions to the denominator change the domain?
- What happens to the domain if there is no square root involved?
- How does the domain change for functions involving cubes instead of square roots?
- How would you solve for the domain if complex numbers were allowed?
Tip: Always check for restrictions like square roots and denominators when determining the domain of a function.
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Math Problem Analysis
Mathematical Concepts
Function Domain
Square Roots
Rational Functions
Formulas
√(x - 8) for x ≥ 8
Denominator cannot be zero: x(x - 9) ≠ 0
Theorems
Conditions for the Domain of a Function
Suitable Grade Level
Grades 9-12