Find The Following For The Given Functions. { F(x) = 5x + 1 $}$ { G(x) = X^2 - 16 $}$(a) { (f+g)(x) =$}$ { \square$}$(b) { (f-g)(x) =$}$ { \square$}$(c) { (fg)(x) =$}$
Introduction
In this article, we will be exploring the concept of function addition, subtraction, and multiplication. We will be given two functions, f(x) and g(x), and we will need to find the results of adding, subtracting, and multiplying these functions together. This will involve using the properties of functions and algebraic manipulation to simplify the resulting expressions.
Function Addition
To find the result of adding two functions together, we need to add the corresponding terms of each function. This means that we will add the terms of f(x) and g(x) separately and then combine the like terms.
(a) (f+g)(x)
To find the result of adding f(x) and g(x), we need to add the corresponding terms of each function.
f(x) = 5x + 1 g(x) = x^2 - 16
We can add these two functions together by adding the corresponding terms:
(f+g)(x) = (5x + 1) + (x^2 - 16)
Using the distributive property, we can combine the like terms:
(f+g)(x) = 5x + x^2 - 15
So, the result of adding f(x) and g(x) is:
(f+g)(x) = 5x + x^2 - 15
Function Subtraction
To find the result of subtracting one function from another, we need to subtract the corresponding terms of each function. This means that we will subtract the terms of g(x) from f(x).
(b) (f-g)(x)
To find the result of subtracting g(x) from f(x), we need to subtract the corresponding terms of each function.
f(x) = 5x + 1 g(x) = x^2 - 16
We can subtract g(x) from f(x) by subtracting the corresponding terms:
(f-g)(x) = (5x + 1) - (x^2 - 16)
Using the distributive property, we can combine the like terms:
(f-g)(x) = 5x + 1 - x^2 + 16
So, the result of subtracting g(x) from f(x) is:
(f-g)(x) = -x^2 + 5x + 17
Function Multiplication
To find the result of multiplying two functions together, we need to multiply the corresponding terms of each function. This means that we will multiply the terms of f(x) and g(x) separately and then combine the like terms.
(c) (fg)(x)
To find the result of multiplying f(x) and g(x), we need to multiply the corresponding terms of each function.
f(x) = 5x + 1 g(x) = x^2 - 16
We can multiply these two functions together by multiplying the corresponding terms:
(fg)(x) = (5x + 1)(x^2 - 16)
Using the distributive property, we can expand the product:
(fg)(x) = 5x(x^2 - 16) + 1(x^2 - 16)
Using the distributive property again, we can combine the like terms:
(fg)(x) = 5x^3 - 80x + x^2 - 16
So, the result of multiplying f(x) and g(x) is:
(fg)(x) = 5x^3 + x^2 - 80x - 16
Conclusion
In this article, we have explored the concept of function addition, subtraction, and multiplication. We have used the properties of functions and algebraic manipulation to simplify the resulting expressions. We have found the results of adding, subtracting, and multiplying the given functions together, and we have presented the final expressions in a simplified form.
References
- [1] "Functions" by Khan Academy
- [2] "Algebra" by Math Open Reference
- [3] "Function Operations" by Purplemath
Discussion
- What are some real-world applications of function addition, subtraction, and multiplication?
- How do you think the concept of function operations can be applied to other areas of mathematics?
- Can you think of any other ways to simplify the resulting expressions in the examples above?
Introduction
In our previous article, we explored the concept of function addition, subtraction, and multiplication. We found the results of adding, subtracting, and multiplying the given functions together, and we presented the final expressions in a simplified form. In this article, we will answer some frequently asked questions about function operations.
Q&A
Q: What is the difference between function addition and function multiplication?
A: Function addition involves adding the corresponding terms of two functions together, while function multiplication involves multiplying the corresponding terms of two functions together.
Q: How do you know which function to add or subtract when given two functions?
A: When given two functions, you can add or subtract them by following the order of operations. If the functions are in the form of f(x) and g(x), you can add or subtract them by adding or subtracting the corresponding terms.
Q: Can you give an example of a real-world application of function addition?
A: Yes, one example of a real-world application of function addition is in finance. Suppose you have two investment accounts, one earning a 5% interest rate and the other earning a 3% interest rate. You can add the two interest rates together to find the total interest rate earned on the combined accounts.
Q: How do you simplify the resulting expressions when adding or subtracting functions?
A: To simplify the resulting expressions when adding or subtracting functions, you can use the distributive property to combine like terms. This involves multiplying each term in one function by each term in the other function and then combining the like terms.
Q: Can you give an example of a real-world application of function multiplication?
A: Yes, one example of a real-world application of function multiplication is in physics. Suppose you have a function that represents the velocity of an object and another function that represents the force applied to the object. You can multiply the two functions together to find the resulting acceleration of the object.
Q: How do you know which function to multiply when given two functions?
A: When given two functions, you can multiply them by following the order of operations. If the functions are in the form of f(x) and g(x), you can multiply them by multiplying the corresponding terms.
Q: Can you give an example of a situation where function subtraction is used?
A: Yes, one example of a situation where function subtraction is used is in economics. Suppose you have two functions that represent the demand and supply of a product. You can subtract the demand function from the supply function to find the resulting profit or loss.
Q: How do you simplify the resulting expressions when subtracting functions?
A: To simplify the resulting expressions when subtracting functions, you can use the distributive property to combine like terms. This involves multiplying each term in one function by each term in the other function and then combining the like terms.
Conclusion
In this article, we have answered some frequently asked questions about function operations. We have discussed the differences between function addition and function multiplication, and we have provided examples of real-world applications of each. We have also explained how to simplify the resulting expressions when adding or subtracting functions.
References
- [1] "Functions" by Khan Academy
- [2] "Algebra" by Math Open Reference
- [3] "Function Operations" by Purplemath
Discussion
- What are some other real-world applications of function operations?
- How do you think the concept of function operations can be applied to other areas of mathematics?
- Can you think of any other ways to simplify the resulting expressions in the examples above?