We appreciate your visit to Given functions tex f tex and tex g tex perform the indicated operations tex f x 3x 6 tex tex g x 5x 4 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the product [tex]\( fg(x) \)[/tex] of the functions [tex]\( f(x) = 3x - 6 \)[/tex] and [tex]\( g(x) = 5x + 4 \)[/tex], we'll multiply the two expressions using the distributive property.
Step-by-step solution:
1. Write down the expressions for the functions:
- [tex]\( f(x) = 3x - 6 \)[/tex]
- [tex]\( g(x) = 5x + 4 \)[/tex]
2. Use the distributive property to expand [tex]\((3x - 6) \times (5x + 4)\)[/tex]:
[tex]\[
fg(x) = (3x - 6)(5x + 4)
\][/tex]
We'll distribute each term in the first expression to each term in the second expression.
3. Multiply [tex]\(3x\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
- [tex]\(3x \times 5x = 15x^2\)[/tex]
- [tex]\(3x \times 4 = 12x\)[/tex]
4. Multiply [tex]\(-6\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
- [tex]\(-6 \times 5x = -30x\)[/tex]
- [tex]\(-6 \times 4 = -24\)[/tex]
5. Combine all the results:
[tex]\[
fg(x) = 15x^2 + 12x - 30x - 24
\][/tex]
6. Combine the like terms ([tex]\(12x\)[/tex] and [tex]\(-30x\)[/tex]):
[tex]\[
fg(x) = 15x^2 - 18x - 24
\][/tex]
So, the result of the function multiplication [tex]\( fg(x) \)[/tex] is [tex]\( 15x^2 - 18x - 24 \)[/tex].
Therefore, the correct choice is:
A. [tex]\( 15x^2 - 18x - 24 \)[/tex]
Step-by-step solution:
1. Write down the expressions for the functions:
- [tex]\( f(x) = 3x - 6 \)[/tex]
- [tex]\( g(x) = 5x + 4 \)[/tex]
2. Use the distributive property to expand [tex]\((3x - 6) \times (5x + 4)\)[/tex]:
[tex]\[
fg(x) = (3x - 6)(5x + 4)
\][/tex]
We'll distribute each term in the first expression to each term in the second expression.
3. Multiply [tex]\(3x\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
- [tex]\(3x \times 5x = 15x^2\)[/tex]
- [tex]\(3x \times 4 = 12x\)[/tex]
4. Multiply [tex]\(-6\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
- [tex]\(-6 \times 5x = -30x\)[/tex]
- [tex]\(-6 \times 4 = -24\)[/tex]
5. Combine all the results:
[tex]\[
fg(x) = 15x^2 + 12x - 30x - 24
\][/tex]
6. Combine the like terms ([tex]\(12x\)[/tex] and [tex]\(-30x\)[/tex]):
[tex]\[
fg(x) = 15x^2 - 18x - 24
\][/tex]
So, the result of the function multiplication [tex]\( fg(x) \)[/tex] is [tex]\( 15x^2 - 18x - 24 \)[/tex].
Therefore, the correct choice is:
A. [tex]\( 15x^2 - 18x - 24 \)[/tex]
Thanks for taking the time to read Given functions tex f tex and tex g tex perform the indicated operations tex f x 3x 6 tex tex g x 5x 4 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
