Math Problem Statement
let f(x)= And g(x)= Find (fg)(x)
Solution
Given the functions and , we need to find the product function .
The product of two functions and is defined as:
Substituting the given functions:
This simplifies to:
Therefore, the function is:
Domain Considerations:
- For to be defined, , which means or .
- For to be defined, , which means .
The domain of is the intersection of the domains of and : [ \text{Domain of } (fg)(x) = [-2, -1] \cup [1, 2] ]
Would you like a detailed explanation of any part of this process?
Related Questions:
- What is the domain of ?
- How do you find the domain of ?
- Can you graph the functions and ?
- How would you find the zeros of the function ?
- How does the domain restriction affect the behavior of ?
Tip:
When combining functions, always pay close attention to the domains to avoid including values that make the functions undefined.
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Math Problem Analysis
Mathematical Concepts
Functions
Square Root Function
Domain of Functions
Formulas
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Theorems
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Suitable Grade Level
Grades 11-12
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