Math Problem Statement
Jawan
Solution
We are given two functions:
The goal is to find the domain of the function .
Steps to determine the domain:
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Identify restrictions for each function: The domain of a rational function is the set of all real numbers except those that make the denominator equal to zero.
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Find the values of that make the denominator of zero: This quadratic can be factored: So, and make the denominator of zero, meaning is undefined for and .
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Find the values of that make the denominator of zero: We can solve this quadratic using the quadratic formula: So the solutions are: Thus, and make the denominator of zero, meaning is undefined for and .
Domain of :
The domain of is the set of all real numbers except the values that make either or undefined. These values are:
Thus, the domain of is all real numbers except , , , and .
Final answer:
The domain of is:
Would you like further details on any step or have other questions?
Here are 5 related questions for practice:
- How would you find the domain of ?
- What is the domain of the function ?
- How would you calculate the domain of ?
- What happens to the domain if one of the numerators had a variable that could also become zero?
- How can you graphically interpret the domain of a rational function?
Tip: Always check both the numerator and denominator for restrictions when determining the domain of a rational function!
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Math Problem Analysis
Mathematical Concepts
Rational Functions
Domain
Quadratic Equations
Formulas
Quadratic equation formula: ax^2 + bx + c = 0
Rational function: f(x) = \frac{p(x)}{q(x)} where q(x) ≠ 0
Theorems
The domain of a rational function is all real numbers except those that make the denominator zero.
Suitable Grade Level
Grades 10-12
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