Math Problem Statement
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Part 1
Find the domain of the function.
f left parenthesis x right parenthesis equals 9 left parenthesis x plus 11 right parenthesis
Solution
The function given is:
Step 1: Analyze the function structure
The function is a linear function, which means it is a polynomial of degree 1. Polynomials are continuous and defined for all real numbers because they do not involve any restrictions like division by zero or taking square roots of negative numbers.
Step 2: State the domain
Since the function is a linear polynomial, it is defined for all real values of . Thus, the domain is:
Would you like further details on any specific part?
Here are 5 related questions to explore:
- What is the range of a linear function?
- How would the domain change if there were a square root in the function?
- How do you find the domain of a rational function?
- How does the domain of a logarithmic function differ from that of a polynomial?
- What happens to the domain if the function involves a denominator?
Tip: When analyzing the domain of a function, always look for operations like division or square roots, as they often impose restrictions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Functions
Domain of Functions
Formulas
f(x) = 9(x + 11)
Theorems
Polynomials are continuous and defined for all real numbers
Suitable Grade Level
Grades 6-8