Math Problem Statement
f(x)=(3x^3+2x^2)/(x^2-x)
Solution
The function given is:
To simplify and analyze this function, let's break it down:
1. Factorization:
First, let's factor both the numerator and the denominator if possible.
- Numerator: can be factored as .
- Denominator: can be factored as .
So, the function can be rewritten as:
2. Simplification:
We can simplify the function by canceling out a common factor of from the numerator and the denominator, but note that should not be 0, as it would make the denominator zero.
3. Domain:
The function is undefined where the denominator is zero. So, , which gives . Additionally, is also excluded because we canceled during simplification.
Thus, the domain of is all real numbers except and .
4. Final Simplified Function:
After simplification, the function is:
for and .
Would you like more details or have any questions?
Related Questions:
- How do you find the limits of as approaches 0 and 1?
- What are the vertical asymptotes of the function ?
- How would you differentiate the simplified function ?
- What is the behavior of as approaches infinity?
- How do you sketch the graph of the simplified function ?
Tip: Always check for factors common to the numerator and denominator before simplifying a rational function.
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Math Problem Analysis
Mathematical Concepts
Rational functions
Factorization
Domain and range
Formulas
Rational function simplification
Theorems
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Suitable Grade Level
Grades 11-12
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