Math Problem Statement
What is the range of x^0.5/x^0.5 -3
Solution
The given expression is:
To simplify, first note that for , we have:
Thus, the expression simplifies to:
Therefore, the expression simplifies to a constant value of , assuming .
Range:
Since the expression is a constant for all , the range of the expression is:
Let me know if you want more details, or if you have questions! Here are five questions related to this concept:
- What happens to the expression if ?
- What is the domain of the original expression?
- How do square roots affect the behavior of functions in general?
- How can this expression change if an additional variable is introduced?
- How do you determine the range of more complex functions?
Tip: Always check the domain of an expression before simplifying it, especially when it involves square roots or division.
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Square Roots
Simplification
Formulas
\(\frac{\sqrt{x}}{\sqrt{x}} = 1\) for x > 0
Theorems
Domain and Range of Functions
Square Root Properties
Suitable Grade Level
Grades 8-10
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