Math Problem Statement
Solution
The given function is:
To find the domain of this function:
The domain of a square root function requires that the expression inside the square root must be non-negative (greater than or equal to zero).
Here, the expression inside the square root is:
Since is always non-negative (because squaring any real number results in a non-negative value), and adding 1 makes the expression strictly positive, we can conclude that:
Thus, is always positive for all real numbers .
Domain:
The function is defined for all real values of . Therefore, the domain of the function is:
Do you want more details or have any questions about this problem?
Here are some related questions you might want to explore:
- What is the range of the function ?
- How do you find the domain of a rational function?
- What happens to the domain if there is a different expression inside the square root?
- Can a square root function ever have negative values in its domain?
- How does the graph of look like?
Tip: Remember that square root functions are defined only for non-negative values inside the root. Always check what makes the expression inside the square root valid!
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Square Roots
Domain
Formulas
The expression inside the square root must be non-negative (≥ 0)
Theorems
Properties of Square Root Functions
Suitable Grade Level
Grades 9-12