Math Problem Statement
Solution
The function given is:
To find the domain of , we need to determine where the function is defined. The main restriction for the domain of rational functions (functions that involve a fraction) comes from the denominator: it must not be zero, because division by zero is undefined.
Step 1: Identify the denominator
The denominator of is .
Step 2: Check where the denominator equals zero
Set the denominator equal to zero and solve for :
Since no real number squared gives a negative result, there are no real solutions to this equation. Therefore, the denominator is never zero for any real number.
Step 3: Conclusion
Since the denominator is never zero for any real value of , the function is defined for all real numbers.
Domain in interval notation:
The domain of is all real numbers, which is written in interval notation as:
Would you like further explanation or details?
Here are five related questions to consider:
- How do you find the domain of a function with square roots or logarithms?
- What happens if the denominator of a rational function has real solutions?
- How would the domain change if the denominator were ?
- Can imaginary numbers affect the domain in real-number functions?
- How does the presence of absolute value functions impact domain restrictions?
Tip: Always check the denominator and square roots for restrictions when finding the domain of a function!
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Functions
Domains of Functions
Formulas
Rational function formula: f(x) = P(x)/Q(x)
Solving quadratic equations
Theorems
Division by zero is undefined
Suitable Grade Level
Grades 9-11
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