Math Problem Statement
when f(x)=3x²-2 and g(x)=1/5x²=4 what is the domain of f+g
Solution
To determine the domain of , we first need to understand the domains of and individually.
Given:
Domain of :
The function is a polynomial, and polynomials are defined for all real numbers. Therefore, the domain of is all real numbers:
Domain of :
The function is also a polynomial (since it is a quadratic function). Polynomials are defined for all real numbers as well. So, the domain of is:
Domain of :
Since both and are defined for all real numbers, the domain of their sum is the intersection of their domains. Since both domains are , the domain of is also:
This means that is defined for all real numbers.
Would you like further details or have any questions?
Here are some related questions you might find interesting:
- How do you determine the domain of a rational function?
- What is the range of given the functions above?
- How would you find the domain of a composite function like ?
- What are the general rules for finding the domain of a function involving square roots?
- How do you find the domain of a function that includes both polynomials and square roots?
Tip: The domain of a function is the set of all possible input values (x-values) that will not cause any undefined behavior in the function, such as division by zero or taking the square root of a negative number.
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Math Problem Analysis
Mathematical Concepts
Polynomials
Domain of Functions
Formulas
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Theorems
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Suitable Grade Level
High School
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