Math Problem Statement
What is the domain of the square root of (x + 81)
Solution
To find the domain of the function , we need to consider the restriction that arises from the square root.
The square root function is only defined for non-negative numbers. This means the expression inside the square root, , must be greater than or equal to zero:
Now, solve for :
Thus, the domain of the function is all real numbers such that . In interval notation, the domain is:
Summary:
- The domain of is , or .
Would you like further details on how to find domains for other functions or any related concepts? Here are some questions you might find helpful:
- How do you find the domain of a rational function?
- What happens when the expression inside a square root is negative?
- How do you find the domain of a function involving a fraction with a variable in the denominator?
- What is the domain of the function ?
- How can you find the range of a square root function?
Tip: When dealing with square roots, always ensure that the expression inside the square root is non-negative to avoid complex numbers in real-valued functions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Square Roots
Inequalities
Formulas
f(x) = √(x + 81)
x + 81 ≥ 0
Theorems
Domain of square root functions
Suitable Grade Level
Grades 8-10