Math Problem Statement
perform (f×g)(x) and (f over g)(x) on this problem
- f(x)=x squared; g(x)=1 over 2 x
step by step clearly and consecutively
Solution
To solve the problem where you need to perform the operations and given the functions and , we'll proceed step by step.
1. Given Functions:
2. Operation :
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The operation represents the product of the two functions, which is calculated as:
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Substitute the expressions for and :
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Simplify the expression by multiplying:
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Therefore:
3. Operation :
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The operation represents the division of the two functions, which is calculated as:
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Substitute the expressions for and :
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Simplify the expression by multiplying by the reciprocal of the denominator:
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Therefore:
4. Final Results:
- The product of the functions:
- The quotient of the functions:
Would you like more details on any step or further explanations?
Here are some related questions you might find interesting:
- What happens to the expressions when ?
- How do you find the domain of and ?
- What is the derivative of and ?
- How would you graph and ?
- Can these functions be simplified further for any specific values of ?
Tip: When multiplying or dividing functions, always simplify the expression by canceling out common factors, if possible, to avoid unnecessary complexity.
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Math Problem Analysis
Mathematical Concepts
Functions
Operations on Functions
Quotient of Functions
Formulas
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Theorems
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Suitable Grade Level
Grades 10-12
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