Math Problem Statement
find its domain
Solution
To find the domain of each expression, we need to determine the values of for which the expressions are defined. An expression is typically undefined where there is division by zero or any other operation that is not mathematically valid.
Problem 3: Finding the Domain
The simplified expression from Problem 3 is:
This expression is undefined when the denominator is zero. So, we need to find the values of that make .
Step 1: Solve for in the Denominator
Set the denominator equal to zero:
Solve this quadratic equation using the quadratic formula, , where , , and .
The two values that make the denominator zero are and .
Step 2: Domain of Problem 3
The domain of the expression is all real numbers except and .
So, the domain is:
Problem 4: Finding the Domain
The simplified expression from Problem 4 is:
This expression is undefined when the denominator is zero. So, we need to find the value of that makes .
Step 1: Solve for in the Denominator
Set the denominator equal to zero:
Solve for :
Step 2: Domain of Problem 4
The domain of the expression is all real numbers except .
So, the domain is:
Summary of Domains
- Problem 3 Domain:
- Problem 4 Domain:
Would you like further explanations or have any specific questions? Here are some related questions to explore:
- How do we determine the domain of a function involving square roots?
- Why is division by zero undefined in mathematics?
- What is the quadratic formula, and when is it used?
- How do we solve inequalities to find the domain of an expression?
- Are there different methods for finding the domain of a more complex function?
Tip: Always check for values that make the denominator zero or cause other undefined operations when finding the domain of a rational expression.
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Math Problem Analysis
Mathematical Concepts
Domain of a Function
Rational Expressions
Quadratic Equations
Formulas
Quadratic formula
Theorems
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Suitable Grade Level
Grades 10-12
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